Finicky boards...
So this one is both your monitor, and it isn't. This problem was most apparent in the 2011 models of the Thunderbolt display which used identical monitors to yours. These LCD's had a bad firmware in one of the LCD control boards which was only recently rectified by apple. Regrettably I am uncertain if your machine would have received this same update. I would encourage you running full updates. Next do these things (but not necessarily in order)
1) reset machine firmware by shutting off machine. After it is off press and HOLD the power button until it has booted to some sort of screen be it gray or what have you.
2) reset smc. shut down machine and unplug from the back. press and hold the power button for no less than 15 seconds. plug back in and boot as normal.
3) reset PRAM. shut down machine. press and hold the following "P,R,cmd,control" turn on the computer while holding these buttons. the computer will reset for as long as you hold the buttons. Continue holding them until you have heard and counted three boot chimes. Release after the third boot normally.
none of these resets will effect your data but it may clear up any bad settings with regards to your LCD. If these things do not fix it, it is likely a bad LCD and must be replaced to help keep your blood pressure down any time you would actually like to see the darned screen.
Good Luck!