I suspect that it is a broken solder joint on the connection between the 1/8" connector and the NJB3 printed circuit board. In order to repair that, you have to open the NJB3, unsolder the backlight, remove the display from the sheet metal clip that holds it and then remove the screws that hold the board in place. The solder joints are on the other side of the board from the display. Once you get it torn down that far, it's pretty easy to reflow the solder joints that go to the 1/8" connector.
While you're there, you could also replace the hard drive with a larger one.
There are lots of threads that talk about replacing the hard drive. Some of those threads also give advice on how to tear down a NJB3. Some people think you don't need to remove the display and that you can remove the PC board mounting screws without removing the display. For no more trouble than it is to remove the display, I don't think it's worth the risk of damaging your display by letting your screwdriver get to friendly with it. It only takes a couple of minutes to move the display out of the way and then there is no risk of damaging the display.
BTW: there are other threads on here that talk about 1/8" connectors that have broken free of their solder joints. Bean will probably be on here soon to tell you not to use Superglue to re-attach it.
Search for "super glue". You'll find the other threads pretty easily that way.