Ideally you would have gotten MSE (or another anti-virus application of your choice) installed within seconds of first connecting the new computer to the internet - yes, before you installed any Windows Updates.
That being said...
I very much doubt that you're seeing the effects of an ongoing infection here.
- What does...
[I had] to restore the primany disk three times now to get the PC [back]
...mean?
- Is it a Dell or HP computer and/or does the computer have an Intel integrated graphics driver [i.e., Igdkmd64.sys]?