Well, it probably hasn't then. So you need to either recap it yourself, or (if you don't know how to solder) send it off to someone to have it recapped.
Recapping is the process of replacing all of the old, leaky electrolytic capacitors on the logic board. You really can't diagnose any further until this is done. Bad caps cause all kinds of weird issues.
to answer your question about the RAM, generally no. Backlit has its ram, and non-backlit has its RAM. There are some exceptions, such as the techknight-designed 8mb board.