Ground braid is for safety. It should be repaired/replaced where broken, but is not required to make the game operate. The signal ground is transferred between boards on the connectors. Best bet is to use a test point ground, or find ground on the connectors for the board in question.

Fast blow glass tube 3/16 amp (0.187 amp) AGX or 8AG style 250 volt (6.3x25mm)
https://www.marcospecialties.com/pinball-parts/F8AG-0.187

Any tinned copper 1/4" flat braid is fine, from whatever cheapest source.

Signal ground is handled by the returns in the harnesses. The ground braid that runs to the rails, the coinbox, and other metal parts is to protect against hazardous electrocution. Many times you'll find an old game with the ground pin sheared off the mains plug, then you have no safety, but the game still operates. Often the braids are snapped at the backbox because of folding the head down - and the game still operates. I'm not sure what your specific situation was, this is what I find in the games I have owned and repaired.

See section " 3n. When things don't work: High Voltage Section Problems " at the link below. Actually, you should read all the tech docs. These not only answer your questions, but there are also some upgrades that should be performed to these boards.
http://techniek.flipperwinkel.nl/ballyss/rep/index3.htm

You might have missed this in the text from the link I posted earlier:
If your high voltage section is showing really high voltage (like 230+ volts), often the 2N3584 and the 2N3440's have failed. The 2N3440's are easy to get. So what can be used to replace the hard to get 2N3584?

There is a replacement transistor, the BUX84. This transistor has a TO-220 style case (instead of a TO-66 case). You may need to enlarge the heat sink's base/emitter holes to make sure there is plenty of clearance for the new BUX84's base and emitter leads. You can also cut off the BUX84's collector (center) lead. You can do this because the BUX84's metal tab, which bolts to the circuit board, will provide the transistor's collector connection. Remember to also insulate the heat sink from the transistor's (collector) metal tab. Use a nylon washer between the transistor's metal tab and the heat sink. Also use a small piece of heat shrink tubing to go over the bolt that holds the transistor to the heat sink.

If you don't want to go through the hassle of repairing the HV, you can always replace the displays with LED aftermarket replacements. Then you don't need the HV section on the supply at all.

The 230 volts you are seeing is before the regulator, which should adjust between 170VDC and 190VDC. Ideally you want to adjust this closer to 170VDC to prolong the life of the displays. If 230 was actually getting there, that's likely to burn out the displays quite quickly, but you said there was nothing at the HV test points on the displays, that's probably because the regulator section is kaputz. If your displays were getting overvoltaged for too long, they may be outgassed already. You might want to post some clear pictures of those displays, because if we can reasonably determine this you might want to make a different choice as to how to go about getting the game going. Original working gas displays are harder to come by, and often quite expensive.

^ This is all good info. Typically I find it justifiable to repair the HV and maybe replace a display if only one is outgassed. Then you can get your original display set up and running for the cost of a handful of parts, at often under a $100. When you have to replace two or more displays and repair the HV, you get up near the cost of a digital display set. With a digital display set, you don't have to worry about another display outgassing in the future, and you don't have to repair the HV on the SDB. It just makes good economic sense for the long run. That's why I suggested looking at or testing the displays themselves first...so if you decided to go the route of digital displays you didn't waste time troubleshooting and replacing parts on the HV.

Do not send the header ouns, this removes the plating. They need to be replaced. Your going to need to repin the female connectors on the cable harnesses regardless if you use original displays or upgrade to digital LED displays.

The high voltage goes straight to the displays. Digital LED displays run off the 5V logic power already present in the harness connectors, this construction ignores the high voltage pins in the connectors. They are plug-n-play.

If none of the rollovers are working, they are stuck off, right? The 3 top rollover switches are in the same column, along with the targets. Are the targets working or not? A4J2-3 is the connector pin number for the entire column, so if none of the targets or rollovers are working, that would be the connector to check. White wire with blue stripe. Also, check each switch to see if this wire is making a bad connection somewhere. The switches are daisy chained so one bad wire can affect them all.

Its a code. A4J2-3. Means board A4, connector J2, pin number 3

A2 P.S. = Power Supply and Regulator board.
A3 S.D. = Solenoid Driver/Voltage Regulator board.
A4 MPU = MPU board.
A5 L.D. = Lamp Driver board.
A1 Dsp = Display Driver boards connected to the score displays.
A8 Snd = Sound board.

You should read the tech guides, that's where you find all this great info . http://techniek.flipperwinkel.nl/ballyss/rep/index1.htm

Deoxit can help, but in the long term is just a bandaid. It won't fix connectors that have lost their spring tension or plating either. You really should get the appropriate connectors and repin them all.

http://www.pinrepair.com/connect/

Take one problem at a time and slow down. It's like getting an old car...and with the miles of wiring, switches and things - you may have many problems to iron out and make it reliable.

The GI is AC voltage. Sound is run off DC voltage. Most "dead" Bally games of this series will have the GI working and nothing else, so why do you say this?

Made me a little crazy for a moment

It's one of those tedious jobs, but its cheap and makes troubleshooting any future repairs *easier* if you are not dealing with flaky intermittent connectors.

When I had my Space Invaders, I replaced every connector on the rectifier and SDB. I also replaced the connector for power to the MPU. I also replaced the connectors to the score displays because they were flaky too.

Repinning and replacing all connectors is a.good idea, but not always necessary...but I do recommend at minimum replacing all critical power connectors.

Varistors, not usually a problem - pretty robust component. You can identify if this is a problem quite quickly using a DMM or voltmeter, see if you have the voltages on your transformer. If all the secondary voltages are there and correct, everything from the transformer to the wall plug is good.

Get a meter and test your connections and voltages at test points. Most likely you miswired or crimped over insulation. Probably isn't even a major problem.

Please don't. Sell it to a pinball hobbyist first. Parting out a game should really be used for very extreme cases such as those already missing a lot of parts, or water damaged and the like. Even then, you'd be surprised what someone can do to restore trash.

I owned a Space Invaders for a little while. It was neglected and dirty but the playfield was in good shape. I did all the proper electronics work, rebuilding and cleaning and sold it at a fair price to a collector at a small profit. People recognize the value of a collectable classic such as Space Invaders when the electronics and mechanics are made to play like they should. I'm am going out on a limb, but my guess is you just don't have the experience or electronics knowledge at this point in time. Give yourself - and the game - a little break. This hobby is learning experience that takes patience and time. Even more if you don't have basic electronics knowledge.
Some of us pinball hobbyists including myself have had many years of electronics training and also have careers in electronics, as well as rebuilding and repairing a lot of these games.

Ok...I am glad you did not give up.

If you do not have the 180V then your displays will not run. For now, let's ignore that and come back to it.

I'll ask a few questions?
Does the game go into attract mode (various lights flashing) ?
Can you coin up a credit with the cabinet coin mechanism (you won't see anything, but you should hear a sound effect)
Do any sounds happen when you turn on the game?

Help with displays:
Check TP4 on the solenoid driver board. See if you have 230VDC there

The test points I suggested were for the original Bally solenoid driver board, it sounds like you have an aftermarket replacement, so test points might not be the same. What board is in this game?
You said you tested fuses with a meter - what DC voltages were you measuring at which fuses?

+190VDC is grey blue wire color. It is pin 6 of the SDB, coming from pin 5 of the rectifier board (transformer)

Screenshot at 2018-12-23 06-05-03 (resized).png

Not likely, but lets get a meter on it and test. First we want to see if we have the AC solenoid voltage coming IN to the rectifier board. Check fuse F4 and reinstall it, then set your meter to AC volts. Check for around 49 VAC across the inputs to BR3 or across VR1 on the replacement rectifier board.

Systematically.

Test rectifier board. Check, you've done this.
Move to SDB board. Check that proper voltages are actually getting to the SDB board. Check output voltages at the board....all good?
Move to CPU board. Check 5VDC logic voltages get there, and make it to the ICs and the game boots up.
...and so on. Leave periphery boards like sound and lamp boards until later in the process, after getting game up and running and playing.

You've got a lot of new boards, so like you said - as long as you have not damaged them probably 95% of this is going to be wiring and repinning. You just can't get away from it.

Take one thing at a time. No high voltage at the SDB board: first check is to make sure the HV from the rectifier board is making it on to the SDB board input. The common problem is the SDB high voltage section need to be rebuilt on older boards. If you replaced this board, that is probably not the problem.

The flippers live before game is started: check flippers relay. This should be off and engage only when a game is started.

For the kicker that throws a ball out of the trough, run a solenoid test and a switch test to check if the trough kickout and switches work or not.

Yes, Ki is usually the flipper relay, at least on the OEM boards, I am not fully knowledgeable on the aftermarket boards, but that should be it.

Please be careful around high voltage. A pinball machine is not worth injury.

F4, yes it is for the solenoids only. The high voltage is rectifier fuse F2 (about 230VDC, gets converted to 190VDC on the SDB and protected there by a 3/16 amp fuse)
For the displays, check to see if 230VDC making it to the SDB TP4.
For the solenoids, check if any are stuck on. Don't forget to check the knocker in the cabinet. These are often fried. Check all the driver transistors. You said this is a new board, correct? If something was stuck on the playfield, you may have already blown a transistor on the board, which would give you a clue as to which switch/coil is a problem.

Oh, and the mess....it's a normal pinball mess, I've seen them all the time

Don't take it personal, but the soldering work in the pictures is not very good. You have also melted insulation on several wires (see orange wire in photographs). I suggest first you learn to solder correctly before you continue working on the electronics.