the battery should do little more than start the car.
It's your alternator you need to consider.
And caps don't do a lick of good in small capacities.
Also, I'd like to note that the power handling of your sub has little to nothing to do with the drain on your battery as it does not generate ANY power, it only consumes it. Your amplifier is the only one of those two that matters.
The power consumption of CarPCs is next to nothing in the grans scheme of things.
You should be fine.