hmm sounds like there's possibly a problem with the screen maintaing connection through the hinge... you might see if there's a "trick" to getting a connection, like a certain angle or applying some gentle pressure at a certain angle or near the hinge.
Long term I say call the manufacturer and see if it is still under warranty or how much a repair or new screen would cost. If it's out of warranty, you may try googling the model number and see if you can find out how to remove the screen/hinge and maybe see if there is something loose you can fix yourself
