UPDATE: I looked up the BIOS on my system, Phoenix Award and was able to google the beep codes - although none of them match what I'm getting (4 short beeps with no pause).
Have you removed all drives, gone down to a single stick of RAM, and removed video card (only if the system has integrated video to fall back on ), and tried a minimal boot? If you get same results, swap to a different RAM stick, if you get same results again try a different RAM slot like slot 1 vs slot 0.
*Is this the same system that needed the battery replaced on the BIOS, now all of a sudden doesnt want to boot? If so.... what happened between last successful boot and when it failed, what action was carried out, any changes to hardware etc.