Most likely cause is the conductors in the data cable between motherboard and screen starting to break down, and making/breaking contract when you flex the cable by changing the lid position.
Spare cables are available, but:
1. They're expensive on any laptop;
2. It's very hard to get them for Sony VAIO laptops.
I can't remember on these whether or not it's a ribbon cable - if so then you're screwed; if not then you might find someone who's prepared to do some fiddly work in repairing the tiny conductors. I have a couple of dead VAIOs in the office somewhere - I'll have a look later and see what shape they're in.
What model do you have?