Wow don't know what to say.

Here's a link to a datashhet for the chip:
http://www.alldatasheet.com/datasheet-pdf/pdf/246793/RENESAS/HD74LS245P.html

In the manual they may only be showing the chips circuits pins and not showing the VCC and ground pins(supply voltage).

Did you pull up the pcb traces(tracks) or pads?
If you don't have a diagram of the PCB, You can use the schematic and a meter and beep out where each pin of the HD74LS245P is supposed to go to. Each pin may be going to several other components or chips so beep to each one.

I hope this is what info you are looking for.
Good Luck and do the work sober.

Have you checked the eproms, the checksum? Did you buy or burn them. They may be corrupt, never know until checked.

gseador, are all power supply voltages getting to the display and sound boards?
Are there any schematics or service manuals on the web for your game. I can take a look and maybe offer some other suggestions.

You also mentioned that when the "sound board boots, playing the "may the force be with you" sound, but then it does nothing else. Interestingly, if I plug in the ribbon cable from the sound board into the MPU (and yes it is plugged in correctly - Pin 1 to Pin1), the game won't boot".

That's kind of strange.

Can you monitor any of the supply voltages on the MPU with the ribbon cable unplugged and with it connected? Maybe the sound board is loading down one of the supply voltages feeding the CPU.

Check my edited post