Ever since I restored backed up campaign save files, I cannot progress in campaigns!

Check to see whether your campaign save files are set with the READ-ONLY attribute on. A file with a READ-ONLY attribute cannot be updated. This can easily occur when you restore OFP's campaign (or mission) save files from a CD-ROM, as a CD-ROM is itself READ-ONLY by definition and this attribute will be retained when files on a CD are copied to your hard drive.