Apparantly adaware and such aren't successfully removing the spyware. Try booting into safe mode (hit F8 repeatedly while the computer is rebooting). Run adaware in there. Make sure you have the latest version of adaware (1.6 IIRC) and the latest definitions.

You could also try installing two other free programs that might help: Microsoft Antispyware beta and zonealarm. MS Antispyware provides constant monitoring of the system. Zonealarm monitors your internet connection to make sure that nothing can successfully get out without your approval. It's helpful in diagnosing spyware problems because it lets you know the name of the process that is trying to sneak out on the net.