It could, in theory, be done; but not very practically. Most Laptop batteries are in the vicinity of 12 volts, so you could use them to run a standard automotive DC-DC power supply. You would, though, need to find a standalone battery charger compatible with the battery in question. Having the charger-battery-DC-DC converter-motherboard 'n stuff chain isn't so terribly elegant in the best of circumstances. More seriously, the last time I saw a standalone battery charger for laptop batteries was when I had a black and white passive TFT Thinkpad with a 386. The other real problem is capacity. I looked up a random battery on newegg (the first one that happened to come up was an 8800mah/10.8volt Toshiba device), which is probably representative enough. 8.8amp hours at 10.8 volts is only 95 watt hours. If we assume that your ATX device will, draw c. 150 watts the battery will be dead flat after just over 30 minutes (assuming perfect efficiency) lower drains would last longer, higher shorter, periods of time, of course. 
Moral of the story: if this is idle curiosity, you might as well give up, it will be a pain. If this is some sort of robot project, you merely have to be clever. If you fancy a carputer, just feed off the car's power systems and address specific questions, at further length, to the enthusiasts on the subject.