Download Troubles

I’m having some problems when I download files. I press save on the file, then I select where I want the download. What usually happens next is the file starts downloading, however for about a week the files have shown 0% and just close. I try to search for them but they only come up as 1kb in application data.

Some things were deleted from this computer about a week ago. All the programs were thought to have been harmless to remove. If something had been deleted would there be a way to get it back without resetting all of the programs and files? Is it even possible to reset it all?