Ground the case of the computer to the car and it will help a little. Make suer eveything is grounded well, the ground wires are short, adn they ground in the same spot. I did this to cure the same problem, but now get a whine from an upgraded soundcard use for surround sound as opposed tosterio; sterio worked fine.
As for the power, I've already left my inverter on for several hours wihtout any problem, and it's 400 watss too. It wire actually even is used to power a reverse IR camera and 5 inch monitor, which I leave on sometimes just for kicks. Just remember to keep cables for a jub just in case, but if the computer is off you should get away with it being on for a while.