Carputer In Explorer

Ok well my cd player just hit the dust in my explorer. Everything still works but it won't read the cd at all so I have come up with a plan. I have a perfectly good working computer sitting around that i never use so I want to put it into the explorer. I just have some questions I need cleared up. Actually as soon as they are cleared up I would like to go to walmart or bestbuy and pick up what I need.

1) What should I look for in a power inverter?

2) How safely can I hardwire it into my Explorer so I don't have to have it plugged into the cig lighter?

3) What do I need to hook up the pc to like a normal screen you would hook a dvd player or xbox to? Will it be pretty crappy quality doing this?

4) What about when I turn the car off? Will my computer just kill?

5) What about all the bouncing around? I was planning to just stick the pc as it is in the back by my sub or maybe under the rear seat. I don't have a smaller case yet or a smaller power supply. Is there anything I could place under it to help eliminate vibration?

BTW, I need a screen but since the primary use of this will just be to control the comp for music I don't really need something of great quality. For what you see at walmart or bestbuy what would you recomend under $200? I can't really justify spending $500 on a screen right now. Yes I know you get what you pay for but what is the best crap I can get for that?

Are polaroid screens any good for crap? I saw a package of two for $180 at walmart the other day...