What happens when you look in Firefox options? Have you tried:
Seeing what the options are at present?
Playing around with the various settings on the "General" tab?
Seeing what happens when you alter some of them, for example setting or changing the "Save files to" folder, or setting "Always ask where to save files"?
Checking "Show the Downloads window"?
Doing some or all of these things and seeing if anything changes might help to shed some light.
Also, when did you do a complete virus and browser hijacker scan? Have you tried starting Firefox in safe mode?
Can you download OK in Internet Explorer?