i don't mean to rain on your parade, because you can do a carputer cheap. but not $80 cheap.
you can use an old computer, but you will have to power it with a dc - ac inverter, or a dc power supply. both of which would cost you >$50.
If you use a laptop you can just run it off of the laptops battery.
But the touchscreen is the problem. Its very difficult to find even used 7" touchscreens for less than $120.