It sounds like the battery in your UPS is dead. You can take the whole UPS or just the battery to a local battery outlet like Interstate Batteries and they'll test it for free. Then you can either buy a replacement battery on the spot or directly from APC. (In my experience, it's cheaper and more convenient to buy the battery locally, but you could check APC's price beforehand.)
Typically APC recommends that you replace your battery every 2 years, but I've had batteries fail sooner than that, and I've had several that lasted much longer than that. Although APC recommends against using other brands of batteries, properly-spec'd replacement batteries from other reputable outlets are just as safe to use as APC-brand replacements.