The only chip which is socketed is the Kickstart - if you're up to disassembling the machine, check that for dirty contacts etc. Sometimes just removing it and reinserting it does the trick. Unless you have an add-on card, there's no clock battery either so don't worry about that. Bad caps are a possibility, check especially the electrolytic ones near the PSU connector at the back left, any showing signs of bulging and/or leakage should be replaced immediately.
If you have any other add-ons connected, remove them and see if the issue goes away. If the ROMs are EPROMS, they might be failing too... Perhaps some small metallic fragments have worked their way under the metal shielding and are shorting out the rear of the motherboard, or the plastic insulating sheet is damaged between the bottom of the motherboard and the RF shield. After that it's possibly a bad solder joint or a failed chip somewhere, but that'd be pretty rare...
