New battery, get them at Batteries Plus for about a third of what APC wants.
I had PowerChute Personal Edition but that wasn't helping. Then my computer started turning itself off at strange times. Oddly, never while I was using it. Then it started shutting down during boot but not if I was starting in Safe Mode. I tried System Restore to roll back to a time before the problems started but that didn't help.
Today, I said the heck with it and wiped the hard drive and reinstalled Windows from scratch. The actual re-install is the easy part, the time consuming part is reinstalling all of the applications and utilities and configuring them as you like them.
Anyway, the UPS is recognized now and the battery options show up in power management so it looks like everything is working fine.
I think that I'll take advantage of the System Image feature and shoot an image of my system in case this stuff happens again.
BTW, thanks for answering.