I saw on a video on utube, that if an virus is allready in your pc, after installing an antivirus, it may override that protection, and actually make a BSOD when attempting to clear the virus.
I always reinstall my windows if it act strange, like BSOD or dont respond well, you should do that too, to be sure that all traces of the virus is gone.
I recently got an infected friends pc to fix, but no matter what i do, i had no options to install any antivirus, or anti spyware, since it disabled vital install rutines in windows, so nothing to do but reinstall windows.
and thats what im gonna suggest you, reinstall windows, then drivers, then antivirus software from a trusted company, like comodo, or AVG or Kaspersky, or norton, then install antispyware, like Spybot Search & destroy.
if pc still act strange, then maybe its a hardware fault, most probably your ram is defect, download a program called
Memtest86 get it here http://www.memtest86.com/
either install on a floppy or a cdrom, and run the tests.(and run it at boot up, then you sure no windows applications is interferring, actually it can only be run from boot up.)
if thats not the problem, maybe its the disk itself, run a full disk test with autorepair, and complete disk on settings.(run it on all disk / partitions you got.)
Then if both complete with no errors, then maybe its your motherboard(though unlikely, since 2 test before would have failed), but then try the everest program (it can test cpu) http://www.lavalys.com/, and do some of the test in there, and if they work fine, you meight have an unidentified virus / mallware in your system still.), and then i dont know what to suggest after that, but to do a total wipe of your harddrive(s), called low level format(find a program from your hardrive vendor).
Hope some help, good luck find your error.
Edit: I had no problems updating or no BSOD trying.