APC make pretty decent UPS. Its not very often that they die.
Have you tried pressing the circuit breaker reset switch on the back?
If you have done that, it could be that the batteries need replacing as, like other rechargable batteries, they only have a certain lenght of life They are around £40-150.
One last thing you could try is a new power cable for it in case a fuse has gone in the plug. They are normally a Kettle plug type. You could nab one off a pc and use that to test.
Failing that and you need to get a new one, Would recommend getting another APC.
APC Back-UPS RS 800VA USB/SER 6 Outlets With AVR & Surge Protection - Ebuyer