Hi dazzerp, welcome to the Sony Forums 
Most cameras with movable screens use a ribbon connector between the LCD and the camera body. The connector is designed to articulate with the screen but over time, depending on usage, the wires inside the ribbon are prone to breaking. It sounds as if this has started to happen to yours, unfortunately.
It's a relatively inexpenisve repair at a local electronics service centre. Some people consider any repair cost is better put towards a new camera. Others (with some techinical know-how) elect to replace the ribbon themselves; there a a number of DIY videos on the internet and the part itself is usually only a few pounds, but it's quite a tricky procedure.
Hope you manage to get it fixed 
Cheers
Mick