Well, that was an ordeal.
After failing to open Windows Backup on my new computer for so long, I sought out different software, spending hours reading reviews. I settled on trying Cobian.
In troubleshooting *that* program (which refused to work for me either), I determined that things seemed to run more smoothly when I had a non-administrator username. I decided it would be a good idea for security as well, so went ahead and downgraded my account to a non-administrator
Guess what starts up just fine now!
Windows Backup sprung to life on the first try!
I am very annoyed. I didn't even change my username, just downgraded my privileges. I really didn't expect anything to change except for it to yell at me more often when I tried to install software.