laptop or desktop?
typically what I would do is take the hard drive out and put it in another computer that has a really good anti-malware program on it. I typically use Microsoft Security Essentials. Run a custom full scan over the suspect HD and then just gather the files I want to save onto another drive.
At first I thought you were seeing BIOS password, but typically it is a black or logo screen, not a pretty picture.
Buying a new computer because of an issue like this is like buying a new car just because someone puked in the backseat of your old one. Good cleaning and you're good to go.