MVP is the file extension for Movie Edit Pro and Video Pro X project files. When you say you cannot open one, how are you trying to open it? By double-clicking on it, or by opening the app and then going to File>Open? What happens if you take either or both of these routes? If "nothing", do you see any error message? Have you tried right-clicking on the file and choosing "Open with ..." and then manually selecting whichever of MEP or VPX you are trying to use?
If so, as you say it's a working file, presumably you have opened it OK before. So perhaps it's corrupted. Do you have a recent backup? Either made by your own backup procedure or the automatic backup made by MEP which saves them with names like your project_BAK1.MV_, your project_BAK2.MV_, etc
Then open MEP with the right mouse method and use File > load backup project.
If it's occurring for every MVP then it sounds like a Windows association problem, but let's leave that for now.
Then did you try Terry's suggestion of looking for those back up files? If there are any, do they open?
If there are no backups then I regret to say I think your project is lost because it would seem your MVP project file is corrupt and cannot be opened by the software. I'm not sure if there is any method by which such files can be restored to "working order".