Here is a JPEG of the display unit in all its resplendant glory, or something. Notice the 'black spot' in the lower right hand corner of the display. This is typical of a first time fire up, performed at testing in the manufacturing process. Please note, this 'black spot' is NOT an indicator that the display is faulty; it is merely the result of the initial fire up - it takes quite a lot of current to kick the display on!

Here is another JPEG (crappy image, I know; my photography skills are somewhat lacking) of the display unit. This image shows, encircled in red, where you would expect to see a glass vacuum seal plug.
If you see a gaping hole here, then rest assured, all the gas has surely escaped and that freaky current/gas chemical reaction can't take place - hence, no lit up display.
Of course, if you can put the gas back into the display and seal the hole then you have your display back. Now, if you know how to do that, then you go for it! Without the right equipment and materials I'm stuck on how to even attempt this.
Another option to fix this would be replacing the display. Seems to me that Jeep had Alpine make thousands of these CD players and yet I couldn't get hold of even one of these displays - new or used.
Now, if you can get one, you're still going to need some fairly specialized tools. You'll need a pretty good de-solderer to remove the old display, lead by lead. Then a good condition soldering iron to solder the new unit on to the circuit board.