IIRC, the 68040 is socketed on that model. I would (very gently and carefully) pop the 68040 out of the socket, inspect the chip and socket, and then reinsert. It could be that there's a little bit of corrosion getting the way, and the rubbing of removal and replacement will probably take care of it.

It won't definitely take care of the problem, but it's a cheap and easy thing to try. Similarly with the SIMMs and VRAM, although problems with those should still allow for a good start up bong, followed by some kind of error or crash.