To be honest, it could be almost anything.
Depending on how far you want to go, how much digital electronics
knowledge you have and what test equipment you've got.
A good starting point is to make sure the +5V and +12V supplies are
running, you can test that with a multimeter. But since the hard
drive is working, they're probably OK.
Make sure all the ICs are seated correctly in their sockets.
Check that the ZIP memory are all in the correct sockets and none of
the legs are bent on a weird angle.
But from then on you'll be guessing. Look for anything visible first,
like corrosion around the RTC battery.
Next you could try swapping parts between a working computer and see
if you have any luck.
An A500 uses the same pair of CIAs, Paula, Denise and Fat Agnus.
After that it's time to get out the oscilloscope and start looking for
a fault on the shared 32 bit address/data bus.
Good luck!