Hi all, I have had the same problem on my mid 2009 macbook pro 13 for years, it comes and goes so I have never bothered to try replacing the screen until recently it got worse. After doing a lot of digging around I found that heat was the common factor. Funny as I had also noticed my fan was staying in slow speed ranges more and more often.
So I have now downloaded the Macs Fan Control app and set my fan manually at 4000rpm, from the moment I did this I have not had the problem occur again and my Macbook runs way cooler to the touch. It seems when they are older something inside is getting hot and the computer is not recognising this to turn the fan speed up.
I hope this can help you too and seeing as its free its worth trying before purchasing any hardware (I've read blogs where people had fitted new screens and its occurred again weeks later). I am very glad I did.
One other habit I've adopted is not placing the computer directly on my lap, I now use a book to isolate me as a heat source.
http://www.crystalidea.com/macs-fan-control
Why can't Apple just admit the fault and advise this?