Can I build a laptop like power supply for my PC with a car battery?
Car batteries emit hydrogen gas and contain acid that can be VERY dangerous for children and pets, so they are not a good choice for using inside of your house. Gel cel batteries are what are used in small desk-top UPS systems, they are a lot safer. 

The DC voltage into your PC must be regulated to within a fairly tight band and as batteries drain, the voltage drops. So you need a voltage regulator / DC to DC power supply. Plus you would also need a float charger.

But if you are going to do that, just get a bigger UPS!