The screen is not meant to be moved from the board like that or at least I would not recommend it.
I would say that loose cable is most likely the problem. Someone might be able to fix it but, I think it is delicate and easily melted.
You can buy the screen without the adapter shield and mega at Sainsmart http://www.sainsmart.com/arduino-compatibles/module/lcd-module/sainsmart-3-2-tft-lcd-display-touch-panel-pcb-adapter-sd-slot-for-arduino-2560.html