Assumptions:
* You are trying to do this on a front loading "slot" type
DVD player for car
* The DVD player does not have a small "pinhole" on the front which would normally be used for manually ejecting discs.
* The DVD player is a type that will eject discs if it can not read them for any reason.
I was able to get my DVD out by:
1. Shut off the DVD player
2. Carefully slide a piece of thick paper (postcard thickness) as far into the DVD slot as you can. It will probably go in only a couple inches max.
3. Turn on the DVD player
4. Wait about 20 - 30 seconds. The DVD player should have trouble reading the disc because it is not spinning, thus it will report an error and eject the disc.
5. If this doesn't work, odds are you don't have the paper in far enough so you are not preventing it from spinning.
There is no guarantee that this process won't harm your car DVD player and/or disc so attempt at your own risk. I can tell you that I've done this several times without damage to either.
Answers from:
How do you manually eject a DVD from a car DVD player? - Answers