Most likely you have a burnt connector pin at the rectifier board, specifically connector J1 pin 7. Also check the 10 amp fast blow fuse at F1.
Measure the voltage at test point TP1 on the rectifier board, it should be around 6 volts DC.

It's very unlikely the problem is at the lamp driver board.

Got your meter in AC?

Did you test the fuse out of the board?

That 7.8VAC listed on the schematic is when measuring E10 with respect to E9. Those transformer wire points do not use ground as a reference.
i.e. meter set to AC voltage, one meter lead on E10, the other meter lead on E9. Infact, put one meter lead on E10 and measure the voltage with the other meter lead on both sides of the F1 fuse. The result should be the same for both sides and will tell you if the fuse is good in circuit without pulling the fuse out.

That's why I asked.

So what about the connectors previous posters asked about.... Have they been replaced?

Sounds like your bridge rectifier BR1 on the rectifier board took a dump

Hmmm, it being a new rectifier board changes my opinion on that BR1 going bad. It's possible but less likely. If you read the voltage of TP1 with only rectifier board J2 plugged in, what do you get? That will be a reading not under load.

Well, then that means it's not the bridge rectifier. Something further up the chain is dragging your voltage down. Could be a broken light socket, could be something on the lamp board. Try this... plug back in either J1 or J3, and test the voltage again. Then try it with the opposite plug (so J2 and J1, then J2 and J3). J1 is your playfield, J3 is your backbox. This will help narrow down where the problem is.

Edit: I suppose the bridge could be failing under load but I think that's unlikely. Others can chime in
Could also try plugging J1 and J3 back in, but unplug J1, J2, J3 from the lamp board and test the voltage again. If voltage is where it's supposed to be, then try plugging in each plug on the lamp board one at a time, see if you can get the voltage to drop. This will narrow down which lamp(s) to check

I'd try reconnecting the rectifier board but completely disconnecting the lamp board. Then plug in J4 of the lamp board, which is power and data, recheck the TP1 voltage. Then with J4 still plugged in try reconnecting J1, J2, J3 one at a time, checking the TP1 voltage each time. J1 J3 are playfield, J2 is backbox.

Others can chime in with more efficient ways of doing this test, but if you do trace it to a set of controlled lamp sockets I think you might have to desolder all of them, then start reconnecting them one at a time to determine which socket is dragging your voltage down.

This sounds more like an open circuit than a short circuit. A short will cause the F1 fuse to glow and blow.

Dismount the rectifier board and inspect the soldering on the E9 and E10 wires and also the soldering on the BR1 bridge legs. Make sure the F1 fuse is in tight, maybe replace it in case it's internally fractured/intermittent.

You reseated your connectors, and now some things are partially lighting, but when they should not, leads me to ask you to verify your connectors are not off one pin or installed backwards. To keep that from happening, verify the key for each connector is in place.

Use your logic probe to check for activity on the four address lines, four data lines and also the lamp strobe #1 signal going into the U1-U4 chips.
The four address lines and the lamp strobe #1 signal are the same across the four decoder chips so only need to check those signals at one chip. But the four lamp data signals individually go to one chip each.

As Billc479 was alluding it's likely going to be a connector issue with regards to these signals (J4 at the lamp driver board or the J1 at the MPU board).

Which Diamonds Flush light are you talking about? Do you mean the 10X light at the top pockets that lights when you make all diamonds?
If yes, it's output #9 of U4
The Jacks 4X is output #8 of U4
The difference between these is address line 0 being stuck low.

Give us more examples of wrong lights illuminating so we can try and see a pattern.

The address and data lines should all indicate high with low going pulses.

Did you by chance mean Aces, *Queens*, and Tens?
If yes, this again points to address line 0 being stuck low.

The pattern I see is lamp address lines 0 and 1 are shorted together.

Most likely happened when you reflowed the pin headers on the lamp driver board. Closely inspect the soldering at pins 14 and 15 of J4 for an accidental solder bridge.

The only lamp that lights when you get all diamond cards is the 10X by the top pockets. The diamond lamp to the left of the centre suite of cards is the "card suite selection" lamp - i.e. it does not indicate when you make a diamond flush.

I think you missed the first half of post #28 above ^^^
Did you check if those pins I mentioned are shorted?

There's a short between those two signals somewhere.

Below I've marked all your lamps working in lamp test mode. They are on outputs #0, #3, #4, #7, #8, #11 and #12 of the four 4514 decoders.
The truth table from the 4514 decoder datasheet shows that these outputs mentioned are selected when both input lines AD0 and AD1 are the same level. Your outputs that aren't working (not being selected) are those requiring inputs AD0 and AD1 to be different - because these signals are shorted, some wrong lamps are being selected.

For example, the upper 10X pocket lamp (diamond suite achieved - marked as mystery score on the schematic and playfield) is output #9 of U4 and requires address AD0 to be high (5 volts) and AD1 to be low (0 volts).
But U4 is seeing both these signals as low (0 volts) and is selecting output #8 which is the Jacks 4X lamp.

At any of the four 4514 chips, measure the resistance between pins:
2 and 3 =
3 and 21 =
2 and 22 =
21 and 22 =

HotHand_LampIssue.png
HotHand_LampIssue_4514.png

It is funny how things work. I found this thread last night, while working on a Hot Hand at a home. Theirs turned out to be all the alkaline damage to the lamp driver board. First Hot Hand I have ever seen too.

I've had a Hot Hand for years and enjoy it.

Yes all those lamp drivers are interchangeable.

Congrats!