Your PC can run 32 bit or 64 bit OS and since you have not filled out your specs it's hard to know what to say really. The only thing I can say is that HP does not have either 32 or 64 bit drivers for your PC but do have 32 and 64 bit Vista versions and your video card drivers are from 2008.
I would consider that your best course would be to download CCleaner and Drivesweeper, uninstall the video drivers and the graphic card in control panel which resets your graphics to 800x600 as it would be in SAFE Mode. Run CCleaner and Drivesweeper removing anything concerning video.
Go to HP and download the appropriate drivers for your PC (remember they are Vista drivers), shut down and cold boot, allow the system to load generic drivers then run the software from HP, once completed go to Control Panel>Device Manager>Display Adapters>Properties>Driver and Update Driver pointing it to where the HP software placed it on your hard drive.