Replace the motherboard, no beep from bios (what so ever) means the board is not initialising. (it should beep 1long & 2 short for video problems)
If any fans are not running smoothly replace them too, otherwise the new board wont last long. If the power supply fan is bad replace the whole PSU.
The capacitors on the bad will have failed, due to excessive heat with the fans running slow. As someone above said the soldering on the north bridge IC may also be bad.