Plenty of motherboards designed to run on 12V only, there are even automotive class computers you can buy. And there is the new 12VO ATX standard put forward by Intel, not many boards using it yet outside of the OEMs, and most of them are still using a proprietary format.
You could also take a regular PC power supply, bypass all the circuitry up to the point it outputs 12V and connect a battery there, the rest of the circuitry should still work.
You can get a 12V to 5V DC DC converter, and a 12V to 3.3 DC DC Converter (which is what high end power supplies use internally these days) and build your own supply.
Plenty of devices for vehicle navigation cheaper than a PC. Old smartphone or tablet with a 12V to USB adapter for example.