Sounds like the hinge mounting points on the LCD cover have broken. You will need to replace the LCD cover and the screen bezel. It isn't terribly difficult to do if you are comfortable with laptop repairs. You will need to remove the screen assembly, disassemble the screen assembly and transfer the panel, webcam, WiFi antenna, etc. to the new cover, snap on the new bezel and reinstall the screen assembly. Otherwise any PC repair shop can do it (not GeekSquad or Office Depot).
Replacement parts are available on eBay, but in order to get new and not used parts the LCD cover would have to be ordered from Asia.
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