First, I'm not a Jornada owner, so I really recommend that you find the disassembly guide online
(http://www.tefs.de/jornada/hardware.php will hopefully work
). But, basically, I'd try to test using your nose and a multimeter. I'd pay special attention to the connection and ribbon that's under the "Jornada" in this image:
http://www.tefs.de/bilder/jornada/hardware680/big/Display.jpg . You're probably at a diminishing returns point; the cost of a new screen or components is going to comparable to the cost of a replacement unit.
I agree there's hope that there's a loose connection since pressing on the right side
(where the connections are seated
) revived things. I'd imagine that it's possible for the ribbon to sometimes bind in that design, giving you an intermittent problem/solution.
Regarding general assembly: These things tend to be clipped/glued together. Any hidden screws will be under the nameplates. Good luck. Handy widgets which still don't have exact replacements IMHO, but starting to show their age...