To test your unit charging capabilities, you can unplug your battery pack and put a DVOM on the outputs. You should see 24V+.
I as well have a Cyberpower, a couple of them actually. Batteries are dead but the unit says fully charged. Even with the batteries pulled out. I'm converting mine into solar generators, but I'm glad I tested these units out without plugging in expensive electronics. You know, the ones they're supposed to help save.