I think the diagnostic bios is actually masking the real problem here. Let me explain here.
When you first startup the Neo Geo, you see a big screen of garbage tiles, the video sync may or may not be in the right range for your display currently. Those garbage tiles appear because unpowered SRAM chips always power-on in an unknown state, as in full of random data. During the Power On Self Test (POST), the VRAM is cleared, the video sync is stabilized and various other parts of the system are tested for functionality.
On the stock BIOS, it doesn't POST, nor does the watchdog circuit attempt to reset the 68k. That is a significant problem.
The diagnostic BIOS, being designed just for diagnosis, probably doesn't care about the integrity of the system, aside from the click of death which can still happen.
Going by that, well the quote from channelmaniac I mentioned doesn't seem to be as relevant since there's no click of death. Stuck at POST can be a dead 68k, probably not since yes it does still work with the diagnostic BIOS. The thing is, that VRAM isn't clearing like it is supposed to, neither on the diagnostic BIOS or stock BIOS. In fact, POST doesn't even happen at all. That's bad.
Now, I'm not that familiar with failed POST situations on MVS boards, but if you've gotten Video RAM error messages in the past, then you could certainly try replacing them and/or check the enable lines for proper functionality. A dead address or data line shouldn't cause POST to fail, but the enable lines certainly could.