speaking as someone that's considered this before, basically what i've figured out is that it's not realistic unless you have a good way to recharge the batteries. unfortunately a vehicle is not good enough. it would take hours to recharge one battery, which would be expensive fuel wise. also, each battery is only going to power so much stuff for a short amount of time. example: small LED lights, probably about 24 hours on one battery with a full charge. a hairdryer (as mentioned above) may only be 12volts, but pulls a HELL of a lot of current through that 12v pipe, so you'd be lucky to get 15 minutes on a full car battery. so you can forget pretty much anything but lights. and certainly nothing like televisions, space heaters, etc.
your only real option here is to get a gas generator, which can run about 300-1000 bucks. then the gas cost isnt so bad, but the cheaper the generator, the LOUDER it's going to be.
if i were you (and this is coming from someone that squatted for quite a while in nola) i would just get a lot of candles and do your best not to burn the house down. also, get a coleman campstove with the two burners powered on propane. makes it really easy to cook a lot, and the little propane tanks will last at least 2-3 hours of cooking time.
also, l.c.'s idea about building your own generator isn't too hard depending on your circumstances... just be careful!