UPS doesn't provide power when it's plugged to the wall

Solution 1:

First, try it in a different outlet - use a grounded extension cord, if needed, rather than move the UPS - to check if the outlet or circuit is bad, rather than the UPS.

If that doesn't help, likely the change-over switch in the UPS is defective. If it were just a fuse, then the UPS would not charge, and/or it would not provide AC from battery. If it has a mechanical relay, it could be as simple as stuck ("welded") contacts, easily pried apart. If it uses solid-state switching, then likely the module needs to be replaced, and it might be less expensive to get a new UPS than to repair it.