Firstly I'd like to take into account that I have absolutely no experience or knowledge of the 'Gameboy Pocket'. Despite that I'd assume their fairly similar, so hopefully there will be something of use to you in this post.
I've encountered an identical problem twice very recently with my DMGs.
Here was the situation I was in
DMG1: The ribbon cable &/or the female cable connecter solder points were at fault
DMG2: The ribbon cable is very touchy and glitches until held in a very certain position
DMG3: Still kicking
I'll start with DMG2 as it was the easier of fixes. The pins on the ribbon cable had small scratches from where the metal had been etched away where they make contact with the innards of the port. Ergo, the lack of available metallic surface became to significant for certain pin/s to function properly. My first thought was to solder the recesses in the ribbon cable pins. This procedure kinda sucks, too much solder on the any one of the pins can easily result in the cable being to thick...
At this point in time, an ingenious thought had presented itself too me. The ribbon cable's pins are excessively longer then needed. I simply cut the pins right along where the etches began making sure to cut evenly so the cable wouldn't fit in sloppy or crooked. After reinserting the cut cable back into the port the screen worked like new again.
Now for DMG1, I went a little overboard with the soldering iron that day.
Same issues as DMG2, except the cable port wasn't sending any screen data at all not even a glitch, and the ribbon cable had even more problems. So with nothing better to do and a lot of time and patience on my hands I went to the next logical step to solve both issues by the mess of wires you see above. After completing all that wiring and verifying my solder work, too my surprise the thing actually came back to life.
I wouldn't recommend doing the latter of the two repairs.
Sadly though after that whole entire process, I look through my drawer and find a perfectly intact DMG ribbon cable I had salvaged a while back. I replaced the wire mess for the new found cable but was ultimately shut down as I seem to fuck up either of the vertical/horizontal cable that connect the screen to its PCB.
[Note: The plastic housing for the screen was melted ended up replacing after the picture also the display worked fine in the last picture. I didn't have an extra backlight so what your looking at is the torn off reflective and polarization layer that I placed back behind the glass.]