If what you're seeing on the screen is just a static random pattern (IE, you turn on the machine and the same pattern sticks there until you reset again) I'd say RAM or ROM are probably your best bets. The CPU is probably crashing shortly after reset, before it can clear and set up the screen area, and the most likely reason for that to happen is it's either:

A: fetching garbage in place of a valid instruction, or:

B: fetching/calculating a bad address from RAM that's causing it to jump to someplace where A: happens instead of where it's supposed to.

(This is based on my experience with repairing a Commodore PET that was "completely dead", IE, static garbage on the screen at power-on.)

If you have an oscilloscope handy the first thing you can check is if you're getting a 1mhz square wave on the PH1 and PH2 pins; the waves should be exactly out of phase with each other.. If you see that then the problem is probably *not* the 6502 itself. (According to the old hands that helped me with the PET the 6502 is a pretty durable part and rarely the cause of a dead machine, but it's still the first thing you check since it's a low-hanging fruit.) After that, well... do you have a parts machine to swap bits with?