::blinks:: the battery would die with in minutes, 5 minutes max of power and that's if the charger keeps it really nice and charged. Best bet is to use a deep cycle Optima yellow top battery, it's used for high end audio systems in cars, also a capacitor would be needed.

Instead of 20amps go with a 40 or 50 amps. I would do parallel so you don't end up hurting other power devices.

Get rid of the lamp, cable modem/router and speakers. The UPS system is there so you can save your work and shut the system off, it's not meant to run the system fully off of battery like a laptop.

If thats what your trying then get a generator.
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To live is to let die