UPS's have a shelf life. The ones I've seen are simply a battery that keeps topped off when plugged into the outlet. If the power goes out and you don't have time to shut the PC down, it's probably a pretty good indication that you need to replace it.
Also, just measure the battery voltage while it's on the motherboard. If you remove it to measure the voltage, you really won't have any idea if it's good or bad, because a voltmeter has an extremely high input impedance and won't put a load on the battery.
Good luck!
FWIW, my motherboard has a bad battery on it too. Hate when the power goes out and I gotta reset up all of my overclocking and date/time and stuff.