It is strange that the board worked previously, and now it acts up. Also strange that the switch matrix would act up AFTER blowing a fuse. If there were any electrical noise coming into the driver board (via inputs from the power supply) they could cause the 4049s, or any of the chips on the driver board to get wonky, and even permanently damaged.

If your drop targets were to lock on immediately upon power up then you'd likely have a bad transistor on the driver board. However, if it comes on later, say after starting a game for example, then it is most likely a bad PIA chip, or even some of the logic chips associated with that PIA.

In my opinion, you need to isolate when this is happening. You won't be able to do it reliably with the on board diagnostics.

I have written some test ROMs (http://pincoder.reversion.ca) that will help you isolate different circuits in the MPU and driver boards. In particular, the solenoids test will allow you to manually fire each solenoid for different durations of time. The documentation for each test should be enough to show you how to run the test, but you can always ask for help here.

You should also run the switches test. Remove the ball from the game, and manually reset the drop targets. If the test shows any switches are still activated then you need to verify the contacts on the switch, and the wiring. If all is good and you still get a reading, you may have chip troubles on the driver board.

The biggest problem with these tests, is that it requires a chip programmer and at least one programmable chip. Let me know if you need recommendations on where to source that stuff, I'm happy to help

You're right, heat does make a degraded chip show its signs of misbehaving, and swapping the board will just tell you the problem IS on the board, but it wont fix the board. Fortunately, these boards are of an era than makes them repairable, as they come with schematics, and each circuit within the boards are pretty straight forward and limited to only a few parts each.

If you suspect the pins on the interconnect, you could test each pin with a multimeter in continuity test mode. If each pin works then you can leave it as is. You could also swap the round ones for the square just to be sure.