Help! Computer acting weird, I run a virus scan and everytime it "quits unexpectedly"

I would be so appreciative if someone could help me.  I'm nervous that a clip art site I went to caused problems.  After I did that the computer acted funny.  I opened Norton and did a virus scan and I've tried 3 times now, restarting my computer in between each just in case that was the issue.  Each time it gets about 10-15% of the way into the scan and dies.  What should I do?