As mentioned, this is a problem that could be caused by leaking capacitors. Have a look on the motherboard for leakage, (it looks like someone has spilled cola on it), as this could be shorting out components. If any is found then it can be cleaned off with isopropanol or another cleaning alcohol.

Another method is to stick the motherboard in the dishwasher but I find that gentle cleaning with alcohol and a q-tip works fine.

This is certainly a cause of problems in IIcx Macs, have a look at one of my RetroChallenge blogs about this issue here.