Doesn't sound like a virus.. almost sounds like a download manager was installed but isn't working properly. Or some spyware gone bad.
Download Microsoft Antispyware and make sure that comes up clean. Go through the add-remove programs and see if there's anything there that looks like it shouldn't be there.
And if Zone Alarm is the only firewall they have don't leave it deactivated for too long.
EDIT: And install Firefox
