I just got a Bally 1980 Silverball Mania that's been in a basement for 20+ years un-played that I am shopping.
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When we picked it up it turned on and only the lights came on. When I got it home and re-assembled it - it was completely dead so I checked the fuses and F6 was blown. I replaced it and it booted- 7 flashes on MPU. But then the power supply started buzzing loudly and F5 blew. I replaced it and then F3 blew and F6 blew again. Each time I replaced a fuse the machine sort of worked for a few minutes until the power supply started buzzing and a fuse blew again.
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My thought is to first replace the bridge rectifier board and then unplug all the other boards and test the outputs. That would let me know if the power supply is bad.

The person we bought it from said it needed a new MPU. The soldered in battery is still attached but it doesn't look like it leaked, however one of the connectors is bad on the side of the battery where it connects to the MPU.
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What do you folks recommend I do next?
I have experience replacing the Bridge Rectifer successfully on a Bally 1978 Mata Hari and it wasn't too hard.

The other thing I'm noticing is that the paint is peeling off small sections of the backglass.
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Is there a way to save the backglass and keep the paint from peeling off further?

I noticed that there's wire soldered directly to a pin!

I will definitely be re-pinning all those connectors - the rectifier board I ordered comes with new pinheaders and trifurcon connectors. I installed this same kit in a Mata Hari machine
https://www.pinballlife.com/mm5/merchant.mvc?Screen=PROD&Product_Code=AS-2518-18

Thought I'd give an update on the Silverball Mania resurrection. Thanks for everyone's advice!

I replaced the rectifier board first - I chose the Homepin Replacement kit from pinball life because it came with all new molex connectors and trifurcon connectors that would allow me to repin J1, J2, J3 and J4.

https://www.pinballlife.com/mm5/merchant.mvc?Screen=PROD&Product_Code=AS-2518-18

The kit requires that you solder about 10 wires from the transformer to the back of the new rectifier which I did by first unplugging J1-J4 and cutting the orange wire that was soldered to one of the J3 pins. Then I removed the old rectifier board by unscrewing the 3 bridge rectifiers and popping the board off. Then I unscrewed the black metal protector around the transformer and the screws holding the transformer to the metal plate. This allowed me to bring the old rectifier and transformer together over to my solder station which makes soldering easier! I followed the instructions and snipped and moved one wire at time over from the old rectifier to the new rectifier.

https://www.homepin.com/kits/ballyrectifierpcb.pdf

Next I re-pinned all the molex connectors that go to the Rectifier board. I followed advice here on another thread and I had already purchased a few tools that make re-pinning easier: Micro Cutters, an Automatic Wire Stripper and Rachet Crimping tool
https://www.amazon.com/dp/B00FZPDG1K
https://www.amazon.com/dp/B01018CX46
https://www.amazon.com/dp/B007JLN93S

Then I disconnected J1, J3 and J4 on the rectifier board but left J2(Where line voltage comes in) crossed my fingers, turned it on and it worked without blowing a fuse. I tested the voltages and they were close to spec. . . however, while vacuuming the play surface of mouse droppings and dust I removed the machine apron and discovered the out hole kicker lever was rusted solid and couldn't move. I pulled it off and cleaned it and realized that the out hole kicker coil is was what was buzzing when I first turned the machine on and it blew fuses. I know when a coil is stuck on, the transistor that switches it on the solenoid board is usually fried. I pulled the solenoid board and lo and behold the Q4 transistor was dead. I replaced it and reconnected J1 and turned machine on and it started without blowing a fuse so I tested the voltages on the solenoid board and they seems O.K. I reconnected J3 and turned the machine on and got 7 Blinks on the MPU and the machine half came to life. However, there were some new problems.

The score displays were wonky unless I unplugged them all except one and only half the lights on the playfield were turning on.
None of the special insert playfield lights were working. My guess was a bad lamp driver board and bad caps on the solenoid board but, the machine did work now without blowing fuses!
After checking all the voltages and test points again I decided to replace solenoid board and the lamp driver board because I would be installing LEDs.

I went with an Alltek solenoid board and lamp driver board.

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On the MPU, I de-soldered the battery and replaced the 5101 RAM chip with a NVRAM Battery Eliminator Chip.
ebay.com link: itm
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After replacing the lamp driver board and solenoid board the score displayed all worked and the general illumination worked but only a couple of special playfield lights worked. Since the lamp driver was new I knew then it must be the connectors to the lamp driver board. I wiggled J4 molex on the lamp driver board and most of the special playfield lights came on. After investigating each wire I found one with a broken trifurcon connector. I ordered this lamp driver repair kit and repinned J4 and it fixed the problem!

https://www.bigdaddy-enterprises.com/repairkits/bally_kits.htm#b-lampconn
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So, all the lights now worked and the machine played! Next, I replaced all the incandescent lamps on the machine with LED lamps.

Next I replaced all the rubber and cleaned all the plastic and I also fixed the play field damage using this decal kit
ebay.com link: itm
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Since the MPU and machine don't have a "Free Play" mode I added a second switch behind the start switch that adds a credit every time you press start.

After playing a few test games I realized something- Silverball mania is a fast game and often the switches don't register.

Next, I am going to add .047 uf Capacitors on many of the switches and I am also going to deal with the peeling paint on the backglass. . .

I had a question about installing the capacitors on a switch. Most switches on silver ball mania have 3 posts. One shielded that's probably hot, one where the other wire comes in and then usually a diode from that post to the actual switch leaf.

Which posts do I solder the capacitors to?

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On Silverball Mania the two switches in the horseshoe and all the letters haven't been registering when the ball hits them quickly.

I drew this pic to be sure I'll be soldering them correctly.
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Thought I'd give the final update on silverball mania. I got the capacitors installed and now quick hits register correctly. I also replaced the flipper switches, pop bumper caps, legs and glass. I also retouched the cabinet artwork.

This game is a classic! I've learned so much working on it. Thanks for everyone's help!