As my original post mentioned, my computer is a MacMini. Power Nap appeared with 10.11.x on the Power tab (not the UPS tab). It's the 4th check box. I've never installed the CyberPower software either. My UPS is old enough that they had software, but the CyberPower website now recommends using Apple's built in software.
Time Machine seems to be working again. In the end, I did the following to get things working.
1- disconnected the UPS and rebooted in recovery mode (no change)
2- ran disk first aid on my time machine drive (found some problems, fixed them, but didn't fix the problem)
3- basically disable spotlight- move all drives to exclude, uncheck all of the search fields. (Time Machine didn't auto start)
3- clicked "enable power nap" in the Energy Saving control panel. (Time Machine started working)
4- reconnected UPS to USB. (Time Machine still working)
5- rebooted. Time Machine continued working and Google Drive started working.
6- shutdown for the night, the started again today, both Time Machine and Google Drive working.