It is quite possible.
The sound board is connected to J5 on the mpu board.
J5 connects to the Peripheral Bus, which leads directly to the 6803 processor.
Any fault on those lines can have this effect I think.
Check the PIA (6821) on the sound board.

Also remove capacitor C12.
Here is a topic about this cap.
https://www.pinwiki.com/wiki/index.php?title=Bally_6803#Sounds_Deluxe_Board

I'll attach the best schematic I could find from the Sounds Deluxe board.

Peter
http://www.inkochnito.nl
Bally_Sounds_Deluxe_schematic.pdf

Good find!

Indeed the cap look blown away.
It is part of the 5V power supply on the board.
Most likely the 7805 (U17) is broken (defective) and needs to be replaced.
That is why you do not have the 5V at TP1.
Be sure the new cap is rated at 25V or higher.
It is receiving 14V (maybe up to 16V) from the power supply.

And another tip, replace the print headers.
If they are not encased in a plastic socket, replace them.
https://www.pinwiki.com/wiki/index.php?title=Bally_6803#Replacing_header_pins