This certainly wouldn't be as efficient, but it would be much safer (I'm assuming you're not an electrical engineer to do the UPS mod correctly):

Buy a deep cycle marine battery, a car battery charger, and a power inverter. This would work fine if you're willing to let your computer go down with a power failure, then boot it up later on your backup setup. But if you want your computer to stay UP during the whole ordeal, yeah, you need a UPS. Buy one, don't try to make one. Heck, I *am* an electical engineer and would be considered technically competant to do what you're proposing. But I'd definitely buy rather than make myself, even though I *could* make if I really wanted to.