I'm trying to build a PC for my car and I need to build a battery in it to allow it to run when the car is off, but to suspend after a given amount of time. The goal is to build a pretty small, fully-integrated computer. Is there a way to build a battery into a Mini ITX case, or do I need an external battery?
It really depends on the case you have.
I would personally get one of solid state picoPSU things and power the PC through a battery. Charge up a capacitor while the car is running, then when the car shuts off let it slowly drain through a resistor to ground and when the capacitor is empty get a mosfet to poke the "power button" pins for it to go into automatic powerdown
Note: I would try to avoid going DC(car) to AC(inverter/UPS) to DC(pc) as you'll loose alot of power that way and inverters always pull power even if they are not powering anything
I think, given the sheer form factor of a M-ITX case you would be better off getting some soft of UPS that is plugged into the car battery and working out how to do a graceful shutdown if the ignition has been cut for more than x minutes. You could try and bodge a load of batteries into a hard disk space but that probably wouldn't be a high enough current/voltage to power a PC.
Also consider a laptop. Inbuilt battery. See if you can find a model that can also take an external secondary battery.