It turns out the problem was indeed the backup program itself. Paragon worked very smoothly for Windows 8.0, but apparently, the 8.1 upgrade made it non-functional, and it was giving me no indication of this fact. So I've been doing backups since the fall which looked just fine but were absolutely useless. When I downloaded the newest version of the software, it would not even recognize those old files as backup archivies. So I wound up having to do a complete clean reinstall. A hard lesson to learn!

P.S. I found a link in a related thread which gave me a way to download a direct 8.1 installation ISO... so it was just one single step, after all.