I always prefer to get rid of things from quarantine anyway, just makes me feel better
I've done a little more investigation, what are the file names in your quarantine ?
Could Norton have picked up on "JS.Exception.Exploit" ?
I spotted this on the Symantec site and just wondered if this was possibly your problem:
"If your Symantec antivirus program alerts you to JS.Exception.Exploit, this means that it has stopped the exploit and prevented it from running. It does not mean that your computer is "infected" with this threat. Rather, it means that the antivirus program has stopped it. Because the exploit is usually not on your computer, in most cases you will not be able to "delete" it, since there is nothing to delete."
This is the page
Even if your infection is not JS.Exception.Exploit, the same can be said in that because Norton has picked it up, means it has stopped it from running, but may be worth uninstalling adaware 1st, then do a norton scan to see if it disappears. If it does, I would reinstall adaware again and not worry if it pops back up again.
Hope this helps a little more?