Well, and I would suggest you get a firewall now, I feel sure that if you had one installed , it would have caught the culprit when you loaded it. Either it or a anti-virus program, ( a good virus program- not McAfee ) would have caught it.
With over 1500 trojans/worms out there ( not to mention virii ) now, you need a firewall at all times. If you scanned with AdAware , it will not detect all trojans/worms, neither is it inherently designed to do so, you will need a deep trojan scanner from time to time.
But as long as you keep reformatting each time, rather than identifying and isolating the problem, you may never know what the problem is.