Based on all that you have done so far, I would say that there are two possible causes for this problem:
- A bad memory stick.
- Malware which keep attaching to your computer, maybe a cryptovirus.
Since your hard drive was damaged, perhaps something else is also damaged. Memory is the most likely thing, based on the behavior you have described.
Here’s a test that would be very easy to run: Go to one of the Linux websites (e.g. http://www.linuxmint.com/), download one of the install files (if you aren’t sure which one, get the 32-bit xfce one), and create a Linux install DVD. Then boot your computer to the Linux DVD you just created. This will put you into Linux Live (nothing will be installed on your computer at that point). Now use the computer for a while. If everything works well in Linux, then there has to be some kind of Windows issue. On the other hand, if you see the same problems in Linux that you see in Windows, then there is a hardware issue with the computer.
If the computer works fine in Linux, then perhaps an answer for you is to install Linux and go with it rather than Windows.