This is a common problem on portable DVD Players when the cable from the lcd to the main board gets crimped or torn. The cable is extremely thin and fragile; it's actually more like a ribbon than a cable. It runs through the hinge and is easily damaged when the unit is opened and closed quite often. If the manufacturer does not thread it properly through or if the unit is poorly designed, that ribbon cable will eventually be torn with no fault of the user.
Unfortunately most parts for portable dvd players are not orderable; Chinese manufacturers simply don't offer service parts. Most portable DVD players these days are simply junked. I don't often recommend buying an extended service plan for electronics but when it comes to portable DVD players (especially no name Chinese branded ones), it's a good idea because retailers such as Best Buy or Circuit City will simply give you a new one. Repairs are simply not possible.
In this case, your DVD Players are stuffed.
atrac
December 2005