I have an old Belkin F6C650-USB-MAC UPS which I used without problem to support some Macs and PCs for a number of years (probably bought circa 2002). I then moved to a house where it wouldn't work because the 3-pin sockets weren't grounded (ouch!), so it was out of use for about 18 months. When I tried to use it in this house, it would not respond at all.
Is there anything sensible to do other than recycle the old one and buy a replacement?
(It's a 120V, 12A unit.)
Sounds like the batteries is dead. I do not have a belkin, but I have changed batteries on a couple of old APC without a problem.
If you're comfortable with taking out the battery, look into buying a small desulphator. I've read of people restoring "dead" batteries with these.
It would be a decent investment, too, since you can use it to extend the life of any lead-acid battery you own (car, boat, motorcycle, etc.).
These aren't snake oil, either. They're widely known in solar, and other home-power circles.
Of course, the UPS could be damaged, as could the battery itself, which the desulphator wouldn't help. You say the UPS doesn't respond at all. Every UPS I've had at least functioned as a decent power filter even with a dead battery. Maybe yours is toast?