I would expect that you could still restore the files in PAF4 by choosing Restore from PAF4's File menu.
My best guess is that you have recently installed software that has associated the .BAK file name extension with its own files.That would change the icon displayed, and double-clicking the icon would try to launch the other program. (Windows hides the extensions unless you ask them to be shown: Tools > Folder Options > remove the check mark from "Hide extensions for known file types" > Apply > OK)
To re-associate the BAK extension with PAF4, try this: Open a folder containing one of the PAF4 backup files Right-click on the file's icon Select Open With Choose Program Always use the selected program with this kind of file (needs to have a check mark) Then open the file with PAF4. This normally works, but since we are dealing with PAF backups and not PAF data files, it may not.
If none of this works, consider installing PAF5 and then restoring the PAF4 backups from PAF5.