Okay. There's a part of the Windows Operating System called the "Registry" which keeps track of what programs should be used to open files which have various "suffixes". E.g. ".doc" should be opened with MS Word, etc.
The dialog which you quoted above suggests that at least that part of the Registry has been lost or corrupted. A re-installation of Windows should help. But there's certainly a question as to what destroyed the data in the first place, and whether it'll be destroyed again, after a re-installation. And, really, nobody can guess that in advance.
One thing to check would be this: if you open a folder in Windows, and check the "Options" (may be under "Tools" ... I'm actually running Linux right now, so I don't have the menus in front of me), then select "File Types", does it seem to have a full selection of file types associated with the "correct" programs? Or do you notice a selection of file types which don't have a program (or the "correct" program) associated with it?