Forget capacitors. I have the alumapro 15 farad thing. Its useless for carputering. Its just good for a big old BUUUUUHHHHHH from your subwoofers. A cap won't do anything for your computer turn on either. If I were you, invest in a second battery. You can get a deep cycle, put it in your trunk, and use a hellraisor http://www.hellroaring.com/ battery isolator to keep it charged correctly. You didn't mention how your carpc is powered. I know that when I leave my inverter on, it will run down the battery.
Do this.. Get a multimeter and hook it up between your battery+ and carputer. If you see any amperage while its off, there is your issue. Some motherboards draw minute power while in complete "off" mode as well as keep usb powered. Put a hard switch on your carputer for when you won't be using it (like overnight). A relay can be used here.