We approach the point where one can only say, a total re-installation of Windows is faster than digging in the deep dungeons of problems. A week has gone, and no obvious solution is apparent.
It's not necessarily a virus problem. To me it sounds like a combination of problems. And they are the most troublesome ones. You could try recovery discs, like badrobot suggests - if you don't have them physically, you may have them in a hidden partition of your computer, the key to open it depends on your manufacturer. But, doing any sort of recovery won't clear your computer of viruses and such, if you have them. To get rid of the dirt, you have to clean it, thoroughly.
It does sound somewhat severe. In case recovery won't work, I would suggest
1. To save your own files you should save them someplace else. An external disk, or DVDs. Preferably save them in .zip or other compressed mode, that way you can check them for infection before inviting them again, but the baddies can't act from compression. To do this saving, you may need help from a friend - since your computer doesn't act properly, obviously?
2. Clear the disk with a low format program,
http://hddguru.com/software/HDD-LLF-Low-Level-Format-Tool/ or
AOMEI
http://www.aomeitech.com/aomei-partition-assistant.html, where you can delete partitions and create new. I would suggest the latter, delete partitions, then create at least two partitions, one for Windows and possible other programs, plus a partition for your own stuff. This way, in future, you have your own material in one place, and Windows in another - when the inevitable comes = you need to re-install Windows, you can clear that partition, having your own things safe.
To clear the disk is the true way to get it to its original state.
Best of all.