I recently bought a dead Jornada off ebay (I wanted it to swap the casing with my rather worn ol' workhorse!) with the same problem. As I was only using it for spares I spent a bit of time trying to get it to work without any luck. It would seem that it is a problem with the connecter ribbon going to the screen - I could get a screen image on the far right of the screen by pressing in a particular point on the cable.
As the ribbon is not something that could be replaced I am guessing that you are out of luck with this. That said there seems to be a fair ol' supply of "dead" Jornada's on ebay with a variety of problems. You could probably pick up one with a working screen and swap over the screens.
In fact this is what I ended up doing with mine. Only days after I got the one off ebay my ol' 568 developed the "missing Safe Store problem" (discussion about this problem on Brighthand
HERE if anybody is interested) so I ended up putting the screen of my old unit inplace of the dead one.
Not sure if this was a case of good timing or of my old machine getting jealous and chucking a bit of a hissy fit
