Hi there. Sorry to hear that your PCs gone down so dramatically - I'm well aware of the frustrations it can cause!
Where do I start as far as the computer is concerned?
It's not often it happens, but you can check for visible signs of damage on the mobo such as small warping or blackened areas. If there are any found, bin it. Similarly the CPU/cooler, RAM, and all expansion cards. It may be too late now, but use your sense of smell - metallic or burned smells, however faint, are obviously bad signs!
Beyond that, strip the machine to absolute basic parts with NO expansion cards (except video if necessary) and NO drives and try and switch it on. It should boot to BIOS, despite warnings.
If you get nothing, check your PSU and replace if necessary (do you have a spare from another PC?). If that's fine, replace the mobo maybe with a CPU compatible version, or replace the mobo/CPU - don't forget RAM. Logically, if the new mobo won't boot with the old CPU, the CPU's fried. A new mobo and CPU may report RAM errors if you stay with the old RAM. Even if not, a RAM diagnostic would be worthwhile.
Once you've booted to BIOS, and are happy with your mobo/CPU/RAM setup, add back expansions and peripherals one by one - start hard drive, then suggest graphics card, networking, optical drives and so on. If they work, great, if not - they got fried in the disaster.
Never come across this question before! I'd suggest very unlikely, and a replacement was the wiser option than continuing to use an UPS that has already failed.