If it looks the same on your A1200 it might be a memory issue as you said, or an address issue (chip pins corroded perhaps) or some other hardware issue.
Normally you would need to show the board to somebody with knowledge of electronics, preferably Amiga, in your area to rule out hardware defects.
Of course you can still try to boot your Amiga without the monitor, just find an adaptor cable to connect it to a tv.
