Check your local Craigslist or other classifieds for cheap old GPUs. Or if you have another PC, borrow the GPU and power supply just to get it to boot.

So March is just eels?

Sounds amazing. Onto the steam wishlist it goes.

Your GPU might be having problems, but the other problems you list sound like either a bad hard drive or a virus / bad windows install.

There are several utility programs you can download that will check your hard drive for failures. I would back up any important files and then run those. If the hard drive is bad, replace it. Either way you will probably want to re-install windows from scratch.