Opening a new tab (Top Sites) begins downloading a file from an old site. The solution: remove the source web site from Top Sites.

Every time I'd open a new tab, my download manager would pop open asking to save an mp3 file. The mp3 file was from a web site that would automatically start playing the music anytime you went to it's home page. <insert long story of chasing numerous ways of clearing cache files and stored settings that didn't work> Yes, a new profile (devoid of any important saved information) worked. But that wasn't a solution, just an avoidance. ... The solution: My new tabs were configured to show my top sites. By sheer luck I happened to notice the source web site of this mp3 file being displayed within my top sites. Clicking the X to remove that site solved the issue.