Reseat any socketed chips for starters....
^^ this.
Check voltages, then reseat socketed chips, then start looking at ROMs.
EDIT: you were too quick ... yes, could be a ROM problem, but do the other two steps first.
^^ and this.
Be very careful when pulling out the rom chips. You want to pull them out evenly, so that you don't bend their legs. IC legs are very easy to bend and break. If you don't have a IC remover tool, then do what I do:
- use a flathead screw-driver bit
- carefully wedge it under one side, be certain you're only under the chip, and not under the socket housing
- lift one side of the the chip slightly by twisting the flathead bit, you only need to raise it slightly
- do the same to the other side, slightly twist again, and eventually you'll have the chip out
While you have the chip out, it's probably a good idea to see if the legs need a cleaning. You can clean them by lightly rubbing an eraser against them. Or a cotton swap, dipped in Isoprophenol.