If you type THE DEAD PC on google it echoes my thoughts on troubleshooting a dead PC. That is, we strip the machine down to its basic 4 pieces (PSU, Motherboard, CPU+HSF, Speaker) and see if it beeps in protest. No beeps and we are looking at the 4 possible bad parts.

The most typical failure given your story is the power supply. You can see if that's it with a Volt meter. Got one?