It is worth attempting repair. You need at least a multimeter, but a logic probe would be a great help. You can make a simple probe with a high-efficiency LED (most today are) and a 1k resistor. Connect the led + side to +5 volts via 1k resistor and then probe the signals by connecting the led - side into signal. Led glows brightly when the signal is at 0, led is dark when the signal is at 1, and with pulsing signals you will get intermediate brightness. Try it out with a working board to get to know it.
(It is better to make the led light from 0 instead of 1, because the TTL chips output pull down to 0 much better than they pull up to 1. You do not want to make extra load to 1-level with the simple probe.)
I think the Bally boards are by far the easiest to repair on bench, due to simple architecture and well working diagnostics. First try to get the onboard led to turn off at boot. If your ROM jumpers and ROM itself are ok then it only needs a reset and clock signals on CPU (with the homemade probe you might see pin 40 of CPU U9 flash the probe at power on, then stay dark, and at pin 3 the probe should light about half brightness).
It is possible that the onboard led driving PIA U11 or the led circuitry is bad, but since your board looks so nice and no battery damage, it is not likely. But you could swap U10 and U11 to be sure.
Usually I like to jumper all my boards to use 2732 in U2 and U6, because that is the most available chip today. I recommend getting an Eprom programmer and maybe also a UV erasing lamp. A TL866CS programmer can be found under $20 from eBay, but beware that not all versions are able to program the old eproms requiring 21 or 25 volts.