Just a guess, but I agree faulty RAM is the first thing I would check. As feef said, the fact that this happened in 1994 would seem to rule out corrosion and similar problems. The only strange thing is you should also see the sad mac on screen. It's possible your VGA adapter isn't configured correctly - I often have a hard time with these. If you can try the adapter on a known good Mac first to configure its switches, then you may be able to see the sad mac error code from your IIcx, which will give you more clues.

Sad Mac chime is actually a good thing: the computer has to boot and run some self-test software in ROM in order to produce that chime. Also it means your sound still works.