DEBBERINSKY 0 Newbie Poster

Some of my desktop icons do not display correctly. I have Windows XP media centre edition, and run Norton internet securing 2006 - I know I know - heard it is crappy.
I tried running TrendMicros free housecall but it closes all by itself in the middle of the scan.
Sometimes my computer turns itself on after I have shut it down, so I have to unplug it from the wall to reset it. I figured all these weird things are signs of a virus, so I have been searching for a few hours for solutions or scans, but nothing seems to work!
HELP!!!