no, I don't think you can get an infection from a not opened email.
you said you use Internet Explorer sometimes, I think you got it this way. because it seems to attack only ICQ accounts there shouldn't be any compromittation of your box when AdAware removed it. "Bargain Buddy" is spyware which also points to IE as source.
well, sometimes it's pretty impossible to say what the source of an infection was, a while ago I had "smitfraud" on my box which steals passwords for a bank I've never even heard of....and I had no idea where I got it from...
that's why you should do regular full system scans and keep the malware scanner definitions up to date...
