I ran into some trouble recently where Firefox would simply not download files. If I told it to open them with a specific application, I would get absolutely no feedback until all of a sudden, the file would be downloaded and the application would launch. If I told it to save the file, nothing at all would happen and the file would never download.
After some snooping I found that downloads are stored in a sqlite database called
downloads.sqlite in the root of your profile (Instructions for finding your profile).
I opened the database and tried to examine its contents but ran into a problem:
Being a fairly impatient person, I simply deleted the file (CLOSE FIREFOX FIRST!) and started Firefox back up. That fixed the issue entirely.