Have you checked to see how the motherboard itself looks? Are there any damaged or leaking (any dry brown stuff on the) capacitors (tubules sticking up from the board)? Try booting with only one stick of RAM, then swapping them (in the undamaged RAM slot) to verify it isn't the memory itself.
I wouldn't htink it is the power supply but you may as well check that also, as it may be a current regulation issue (if the RAM slots are getting burnt).
Lastly, see if you can find a manual for the board online that may tell you what the beep errors on bootup mean.
Who made the motherboard? (I.E Asus, Gigabyte, etc)
Remove and re-insert the C-MOS battery and see if this helps to reset the BIOS - is is perhaps Overclocked??
Hope this helps!