The FPC connector may be broken, so that the wire looses connection.
You can buy a new one here: http://www.parts4repair.com/htc-one-x-lcd-screen-fpc-connector/
I have done that myself and resoldered the new connector. Though, it requires some soldering experience.
If you are lucky, it could be that the clip that holds the wire is damaged or misplaced. Open your One X and check. The fpc connector is the connector he is de-connecting at 3.51 in this clip http://www.youtube.com/watch?v=P8SpHbhzLgU.
Follow the instructions in the video to open your One X