Hey I don't know if you still need an answer but i've managed to fix my Ipod Video with the same problem. I did it the cheap way and with Super Glue!
Basically I broke the retention clip off the LCD connector which is on the logic board.
I found that I needed the LCD display to be on in order for Itunes to successfully detect my IPOD, and use it (obviously).
Because the retention clip is missing, it means you can push the ribbon cable all the way "through" the connector and it won't get contact with the pins on the logic board, this is why with mine when you push the ribbon half way into the connector it'll light up, but then when you push it all the way through it goes black again.
What I did was, and it's incredibly easy, is push the ribbon cable into the connector with the missing retention clip, hold it in place so the screen lights up, and applied superglue to the connector and edges of the cable, and it worked fine. I did this while my ipod was on and connected to a computer. I didn't really care if I stuffed my ipod completely though.
Can post photos showing it going/ with the cover off and missing retention clip if needed.
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