Old battery's probably swelled up and that's why it's getting stuck. Don't be shy about removing the entire top cover and front of the frame, if needed.
I have a (refurbished) APC Back-UPS LS 500 I've been using for a year and a half or so, and recently when the power's been crappy (thanks to bad drivers...) I've noticed it's no longer doing the thing ...
For mission critical business systems, UPSes are a critical necessity as a single brown out, power surge or power outage could easily cost thousands of dollars worth of lost time, lost data and ...