Curious, why rewire a UPS to do this? If its a matter of the UPS being available 24x7 in order to power down you PC, you should have that already - switching out the UPS battery for a marine battery voids the warranty and makes the UPS begin to operate in an unwarranted and possibly dangerous configuration. I would rather take the deep cycle marine battery and apply your wiring skills to create a hot back up power supply: so you should plan to power down your PC like any other UPS user, and then maybe power it back up with your separate but more rational marine battery power backup. I'm sure there are videos out there to get you started. I do appreciate the impulse to tinker. I am electrically deficient myself, but I suspect I could match up the right inverter and connections to power a few necessaries - like my ham radio if I had a hankerin to do that.

Trying things at your own risk is just that, at your risk - god bless you and your local responding fire dept if you get this retrofit wrong.