Think i've heard this story a few times after a steam install, so i would advise to begin there, ideally clean everything and go back to a restore point.
Basical general steps.
1- Save what needs to be, work, photos, etc, knowing that if its a virus it can be corrupted, so take care when you use your saves again
2- fall back to any steps you have taken, such as installing steam. Erase every trace of its existence. No just uninstall, earse also the files it has installed by hand.
3- norton sucks. Use antivir, avast, or if you really feel like paying kaspersky is the only good one worth to pay for ( wich doesn't mean he is the best ). I recommend antivir as a secondary one, he detects a lot but stops little lol. There are classifications of the best stuff per year on the net, just check they are neutral.
4- antivirus is not enough. Use a firewall. Preferably Comodo Firewall.
5- there should be a log somewhere, a txt file recording what;s up with your computer, or you should be able to launch something showing it to your in real time, try to find this stuff via google. If it exists. Not sure how windows manages this. Haven't used it in aaaaages. I use sometimes my linux terminal to display everthing happening in my computer real time, or just parts of it, matrix style, very useful in such cases.
6 - Wouldn't go for the hardware, nor for a virus, none would give you usually such results, i would go for a weird bug.
7- when computer problems happen, it is recommended to post your config ( OS etc ) and the log ( after you have read it ) if you have any ( if too long host it and link it )
Note that i am not using windows anymore, but several various Linux, so i won't be able to help you much on the windows specific help.
If i remember correctly it is just some crap created by steam in rare cases and even cleaning it completely won't reverse it, you most probably have to get your hands dirty by messing around with some files, which should fix the problem.
Edited by vegan cyberpunk - 12/1/12 at 5:46am