Bally lamp driver not giving voltage on certain switched lights

Usually, you can look through the connector with a bright light from behind to see if the knuckles of the crimp pins are caved in or missing. Good pins tend to almost fully block the passage way.

The board doesn't supply voltage to the lamps, it's purpose is to provide a path to ground for each lamp. The only voltage on the board is 5V for the logic.

Check the wiring under the playfield that daisy chains your non-working lamps together. At the end of the bare wire there should be an insolated wire soldered on, which comes from the rectifier board. Either the wire has broken off or there's no connection in the plug on the rectifier.

Yep, the common braid wire between the feature lamp bases is 5.4VDC from the rectifier board.
If you ground the colored individual wire at the tip of the feature lamp sockets, you complete the circuit and the lamp should light up.
Same if you ground the lamp wire in the connector at the lamp board. And same if you ground the metal tab/anode pin on the SCRs at the lamp board.
Running a jumper wire from TP3 on the lamp board to the Gate pins printed on the lamp board PCB as "G" at any of the SCRs will manually switch on the SCR and activate the respective lamp.

If you measure the voltage at the lamp connector pins on the LDB, you should be measuring 5.4V. The path of least resistance is through the lamps to the 5.4V supply rail on the playfield and you've basically measured open circuits. This indicates the problem is between the lamp board connectors to the lamps, not upstream from the LDB to the MPU board. Any chance there's an intermediate connector on the cable harness between the lamp board and the playfield that isn't plugged in?
What happens when you ground one of the "faulty" lamp connector pins at the lamp driver board itself? If the circuit to the lamp is good, the lamp should light.

As Quench pointed out, if, with your Black Test lead on Ground and your red test lead to one of the Lamp Drive output pins on the Lamp Driver board, you get 5.4V (and the light is not lit), you have confirmed that the light is getting 5.4VDC, the bulb is good, the lamp socket is good, and that the wire back from the playfield is good to that pin. In the case of a working light that is lit, you would get nearly zero volts.

The SCR grounds the lamp wire. You can do the same thing to test the wiring from the Lamp Driver board all the way back to the lamp by grounding the pin at the lamp driver board connector. By switching to putting your meter on 5.4V and then checking the same pin with the lamp lit, you will get 5.4v. But, if the lamp is not lit (like your bad ones), you will get 0VDC.

It sounds like you have already found some dead drives in common with same channels on U1-U4 which can translate to a lack of one of the 4 data bits geting through to the ICs (or one or more of U1-U4 holding down that Data pin). IF you know the Lamp Driver board performs perfectly in another game (which means U1-U4 are good), then your problem is either:

Bad Connector (female pins) on the MPU board feeding data to the LDB (sounds like you repinned the connector).
Bad Connector (female pins) at the LDB feeding the Data to the ICs.
Open wire from MPU to LDB (highly unlikely).
A Bad output from the PIA on MPU board responsible for that dead Data bit.

IF there is nothing in common with bad lamps related to U1-U4 then it is possible you simply have a bad IC. But again, not the case if your board has been confirmed good in another working machine.

A logic probe would be helpful.

Here is a thought: After putting the game in lamp test, try unplugging the two connectors on the right side of the MPU board (Cabinet and Playfield Switch matrix) and see if your light problems change???

The data is repeatedly being updated and clocked into the latches. Which requires not only tying the 4 data lines high or low, but also the 4 address bits that address one of the 16 latches inside the MC14514's. So, in my mind, its not really worth trying to do this. I find it easier to simply probe the lines from start to finish.

If you can find some common-ality to all the lights that don't work (won't light or stuck on all the time), then you might be able to narrow it down to just one of 4 data or 4 address lines. Once you have done that, then its a matter of checking continuity from where it starts (Pin on PIA in MPU) to where it ends up (Data inputs on ICs). Taking into account any resistors that are used between the ICs and the output pins on the connectors. Beep test is not as good as actually reading the ohms value and possibly comparing it to one of the same types of signals that you know is getting through (another data line). Again, a logic probe makes this kind of troubleshooting much easier since you can see highs, lows, pulses and possibly floating lines. A DVM is not really very useful in this case. Of course, an Oscilloscope is much better.

You will see that PA5-PA7 from PIA U10 become PD0, PD1, PD2 and PD3 (lamp data) at J1. PA5,6, and 7 are also used to select the dipswitch banks. They go to J4 on the lamp driver board. And then feed each of the 4 Latches as "I" at pin 23. The Desired output is selected (addressed) in all 4 Latches via AD0-AD3. These start out at U10 as PA0 - PA3. Which are also used for Playfield switch matrix output strobes. Which is why I suggested unplugging the cabinet and playfield matrix above after putting the game in lamp test. A grounded switch strobe at the coin door or on the playfield can hold a Lamp Address strobe low causing issues. This sometimes shows up as a Slam Switch weight touching the coin door (no more mylar insulator sticker) or a stuck coin switch.

You will note on the Lamp Driver board, the Data and Address lines have series resistors R71 through R79 which are 20K which is why you can't use continuity (Beep) test. So you pretty much have to start out at the 6821 PIA (U10) pins and ohm them out to the male header pins (taking into account the 1.2K resistors used in series with the output as part of a resistor/capacitor filter. Then, from the resistors or back side of the board male pins to the back side of the board to male pins on the Lamp driver board (pretty close to zero ohms for all since it is direct connect wiring). Then, from the male pins into the lamp driver board (again, through 20K resistors) ending up at the pins of each IC.

There is also a page in the manual/schematics that show you the wire connection from one board to the other. The one attached here is from Space Invaders.

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Okay, so now try one or the other. Remember, one is the Switch Matrix wiring to the Playfield while the other is for the lower cabinet. This way, we can find out which one is loading down the data line.

J3 is for the cabinet, J2 is playfield.