When you plugged the screen into another computer and used a different monitor on your carpc, did you get an image? I'm not quite sure form what you wrote.
*Edit after re-reading it, it seems you get an image when using another monitor on your carpc, but the monitor still doesn't work when you're using the screen on another computer? I had an issue once, where the little round din connector wasn't connected properly even though it was done up. I've found that you can't rely on screwing it tight enough to connect properly. You really have to push it in tight first, then just tighten the nut to secure it there.
This picture I found is pointing the connector I'm talking about.