--- I had successfully moved the files AND the Sony still worked! I then tried to reinstall the HD, but I had to unplug it one more time. When I restarted, it wouldn't recognize at all! Nothing worked. Any ideas?
Congratulations for getting your data safe! Back to the problem: Is it a desktop or a laptop? Do the fans rotate at startup? If there's no life and if it were a desktop, I'd say it's the PSU. After that were sorted out, the motherboard; either capacitors or chipset. If the fans whirl, it could also be the GPU or RAM.
As for laptops, I've seen the chargers fade to the point where they are capable to light the charge led, sometimes they may even charge the battery during a long period so that some tasks can be performed until the battery runs out of juice. That can be confusing if the charger is plugged into mains. So, actually, the list above also applies to laptops.