A death chime before the startup chime - I think that's our biggest clue at the moment. There's something setting a sad mac before the video gets initialized. RAM verification and ROM checksum are the only 2 things I can think of. ROM checksum could fail because of actual damaged ROM (unlikely) or damaged higher address lines to the ROM. We know that low address lines and all data lines are okay to the ROM because it successfully plays a death chime. But I really don't think it's ROM-related at all, that would be really bizarre.

I think I'm with technight and leaning toward something RAM-related. There's no other particularly fixable alternative that I can think of. I guess you could try cleaning the RAM fingers and slots and replacing the caps but I'm pretty much at a loss otherwise. Actually, you might be able to apply pressure in various directions to each RAM SIMM to see if you get a temporary good connection. Also, pressing on chips on the logic board, etc. But it's all just reaching for clues at this point.