If you can't see the BIOS then it sounds most like a MOBO / processor failure (or L2 cache failure).
Normally RAM module failure will be detected during the POST, but an on-screen alert will be displayed, even if you can't access the full BIOS routine (due to no memory).
Given power - and lights - but no sound effects, I would suspect processor. Have you tried re-seating the processor? Last ditch effort I know.
If it turns out to be the processor and you get a replacement, try to find out why the old one failed - so that it doesn't happen again. As pba_target suggested, ensure you have protected power supply, also adequate ventilation and dust protection.
BTW, I have come across servers that will not boot (to protect the CPU) if the cooling fans are not running. I once spent ages tracking down a CPU / memory / mobo problem that turned out to be as simple as a disconnected power lead to a CPU fan! But I doubt that standard desktop PCs would have that "protection".