If you put a piece of cat 5 in series with your battery cable, and start the car, you will either start a fire, or the solenoid won't kick in as the current drawn from your starter will burn the thin cable instantly.
mind you the voltage at the other end of your cat 5 will be about 0.5 - 1V as the load is so great (200A or so on average) drawn from your starter, that the cable it basically shorted to the battery terminals. WRT the negitive term.
So in answer to this post, heavier gauge cable will prevent a voltage drop to your PC and therefore stop shutdown of the puter when you are cranking, or idling at the lights.
an average PC will use about 3.5A to 6A @ 12V. say it's 4A for an example.
if a cable has a resistance of 0.1R (ohms) per metre, and it's 4.5 metres from your battery to the puter, then the resistance of the cable is 4.5 * 0.1 = 0.45R.
Then the voltage drop over that piece of cable is....
0.45R * 4A = 1.8V
This means that the voltage at the inverter is 12V(battery) - 1.8V(cable loss) = 10.2V.
Not quite enough if you want to start your car as well.