I needed a backup battery solution for running some medical equipment in case of mains power failure. Nothing life-critical but still useful to have just for a few hours in case.
So I bought a 600w inverter for about $79 so that was a good deal you got. I ended up buying a regular car battery that is the same as my regular car battery just so I have a spare at least I can also have it for the car so I feel better about spending the money, but it turns out it would have been better to buy a marine type deep cycle battery. The car batteries will not last for heavy discharge cycles and don't charge up and get ruined if they discharge too much... The lead plates get warped, they are thin and damage permanently. So for running a backup that may take a long time and plan to use up all the battery juice, best to use deep cycle because you can't really use the full capacity of the car battery without ruining it.
I also got a charger and I need to charge up the battery about 1-2x per week from the outlet otherwise the battery also drains and gets ruined. Deep cycle battery would be better, but then I wouldn't really have a backup for my car. The advantage of car battery is it delivers high amps for the initial alternator draw needed for starting the car, just for a fraction of a second it can handle the load. Then it goes back down to normal amps, since it has more and thinner plates inside, but the problem is the warp and sulphide bridges (I think they are called) short the battery eventually and kill it, even the conditioning setting on the charger can't bring it back to life.
I would suggest buying another battery equivalent to your car, and charging it up right up until you have power from the outlet. Then if you have any access to an outlet from a friend or work or public place (if you can get away with it) rig up a suitcase with wheels and put the car battery and charger in there, and go charge it up when you need from mains power. I would be wary of using your car battery for too long because you will kill both your power and means for travel, especially if for survivalist strategy. You will be wasting money burning gas and that will start to add up too. Best to use another battery if you can get one, rather than rely on your only car battery. Maybe some mechanics in the area have some cheap batteries around.
If you are just charging up your Blackberry then it is fine, and maybe think about LED flashlight or even those hand-crank ones so you need no power at all. I would recommend one of those Eton radios with flashlight and crank and Usb plug which you can even use to charge devices as well. For heat I would suggest getting a bunch of warm clothes and many layers. Your body heat in the car and sleeping bags should provide plenty of warmth.
I don't suggest using a microwave oven. It is not critical and will waste a lot of power. Start thinking about how you are going to provide food, consider buying stuff you can eat at room temperature. It may not be ideal but you are trying to survive. Bread, peanut butter, cans of tuna or fish and other stuff, cereals, etc... There are lots of options that should keep you going for a few weeks and you won't starve. But running a microwave out of a car, not too sure as those are high watt items. If you kill your battery trying to heat up some food that cost $10 then you'll be pretty pissed. If you are in civilization consider asking someone to warm up your food for you, I'm sure they would not mind depending on who you know and where you will be parked while you are living out of a car.
Good luck, let us know how you make out.