Windows 7 Bluescreening on Old Computer

Hey guys, having some issues with a friend's computer. His brother built it and it was running a pirated version of Windows 7. I think it ran fine for him until recently it started asking for authorization. I told him to just get an OEM version of Windows 7 for $110 and throw that on there. He did and now it randomly bluescreens when windows update is run.

Here are the specs:

CPU: Pentium D @ 2.8 Ghz (Smithfeild)
RAM: 1.5 GB
MOBO: Microstar MS-7187
VIDEO CARD: Radeon HD 4350

I've done the following to try and figure out what's wrong:

- Ran MEMTEST on it (7 passes) and it passed.
- Ran HDD diagnostic tool off Ultimate Boot CD and it passed.

I also ran HW Monitor and the CPU was around 60c, I have no idea if that's out of the ordinary.

Any help would be much appreciated!