Hi elan,
Well, Like Kipass said it won't last 6-7 days but it should last a good day w/o power. I have one of those boat 20 hour trolling motor batteries. It was about 60 bucks at a Bass pro shop and then the inverter came from best buy.
Jensen 300-Watt Power Inverter
Model: JP30
With 300 watts continuous power output (600 watts peak) you can power anything from a laptop to a TV/VCR combo. Ideal as an alternative power source for boats and RVs.
I've never had to test it yet due to powerfailure, (KC Power) has been good) but I do have a boat I use it on and when I camp it's great. Since i use that for camping I thought it was a great idea incase I'd lose power here as a back up for my reef tank. As far as keeping it charged I just use a standard car battery charger and try to keep it fully charged at all times. I think it'll get me by. Best of luck
(and yes, I do need to test it when I get some time to see how long it will go... that's a great idea that I should have done long ago; I'm such a procrastenator sometimes.. It can't take more amps than a trolling motor though and that's 20 hours)