Belkin Backup battery

Can try Belkin or Batteries Plus or other online options.

OR buy a replacement UPS instead of the Belkin. 

https://www.nytimes.com/wirecutter/reviews/best-uninterruptible-power-supply-ups/

https://www.techradar.com/news/best-ups

Go to the Belkin site and see if the offer replacement batteries for your particular model. I use APC UPS's and just replaced my battery with an original one from APC. They even send a box and return label to safely return the used battery for free.

ATT won’t replace batteries on their own equipment?

@jenniinla 

Nope, batteries are consumer items not ATT equipment. ATT stopped providing batteries in 2015.

For most, the battery function  was to provide up to 4 hours of standby time for Uverse Voip (home phone) service, not for internet or TV services.

now it has stopped blinking.  Do I still need to replace the battery? 

If the battery is more than three years old I'd replace it.