Typing THE DEAD PC on google finds the usual advice so I won't duplicate that here. When you post you may want to consider the forums are all volunteer and while your story about getting files out tells that there may be hard drive issues, not a word about the PC make, model, age, etc.
The only clue I can use is the NO BIOS SCREEN OR BEEP. My kids machine will do that when we leave some USB device plugged in. Try this. Unplug all USB things and try again.
This past weekend I left my computer on overnight, in the morning I went to use my computer and nothing was happening. I had to turn off by holding the power button. When I restarted my PC, the CD ROM drive spun, however did not access the Hard Drive nor did it show the BIOS or beep.
I then took out my hard drive out and used a SATA/IDE connector to access my hard drive using a USB on another computer. The drive is partitioned into 2 drives. I was able to access the D drive and copy files off of it. I could also access and browse the C drive (windows), however could not copy any files - received the following error message:
"Cannot copy file: Cannot read from the source file or disk".
I then hooked everything back up, reseeding the ram, and cables. This did not help. I also put in my Windows CD to launch the windows repair, and this did nothing, just spun the disk.
Any suggestions to fix this? If you need more technical information let me know and I will get it.