I once recovered a business PC that wouldn't boot, and they didn't have backups of course. The problem was stiction*. The motor didn't have enough oomph for the initial start-up of the drive. I removed the drive, but left it connected. As soon as I applied power, I gave the drive a little rotational spin with my hands helping with the start. THEN they did their back-up and restored everything. This obviously won't help at all if the heads have crashed or the electronics are fried, but if you don't hear the drive spinning it's worth a try.
*Stiction - resistance to initial move. Try moving a full glass slowly across a table. If you move it very slowly it will probably move in fits and starts. Once you get it going at a better speed, it should move smoothly, as evidenced by the liquid in the glass.