Screen blank when working in OSX but works fine under windows 8.1

MacBook Pro 13" 2011 A1278 (i5 processor)

Hi,

I have a problem with my MacBook Pro 13" I have partitioned the SSD drive with both Windows 8.1 and OS-X Yosemite. I use the option key to pick the OS I want to work in.

A few weeks ago I restarted my system at which time I could not see anything on the screen the lights on the keyboard came on as per normal and the fan was working.

I plugged in an external screen and it worked perfectly. Then I restarted again in Windows 8.1 and internal screen works, and so does external screen. But, systems internal screen will not work in OS-X. At the moment I'm using system only under Windows 8.1.

I took it to the "Genius" guys at the Apple Store they said it needs new board, and wanted $500 to fix it!

How can there be a problem with the board if it works with Windows 8.1 ???

I have a technical PC background but this issue I just don't understand. Someone out there must be able to shed some light to this issue.

Please help... Thank You