Wait won't the car battery be pushing current into the computers 12 volt power supply output.

So I think I would need a diode and some resistors between the car battery and the computer power supply.

I would think current would flow into the output of the power supply because the battery has so much more voltage then 12 volts.

It would blow up the power supply

so now i don't agree with the person that said it is possible

 

Here are a couple links that may explain things about charging a 12v DC car battery.
The diode section is what is referred to as a rectifier circuit consisting of six diodes. The alternator in a car produces AC voltage, The regulator adjust's the output voltage to maintains approx. 13.5 to 14.4 (target is about 13.8v) The amperage is generally around 100 amps or so.
The battery takes what it needs and the alternator will produce what it can.
Because you are coming out of house, I strongly agree with ALL previous posts. However, if you were to make it as an alternator on a vehicle, A bridge rectifier and a voltage regulator would work as far as converting the AC to DC and regulating the voltage BUT I am speaking as a mechanic not an electrician. I can't really tell you if AC from a home outlet would be a good idea using this same method. I can however tell you that I have had the battery charger from the shop apart and that is one massing transformeR inside! I think it is a good idea to listen to these guys.
When I was a kid, I plugged my speakers in the wall outlet.

Anyway, here are the links
http://www.bcae1.com/charging.htm
http://www.allaboutcircuits.com/vol_6/chpt_4/8.html

ONE MORE THING TO ADD, PLEASE BE CAREFUL!