My year old sony vaio vpc ee31x has a white/blank screen how do I fix it?

I have a year sony vaio ee31x laptop, more than a month ago My screen would just go white either when I am working on the laptop or when booting up, then it would show after a few mintues and the go white again. I recovered my laptop to factory settings and it worked fine for another five weeks. On Friday the 16th of March the white screen problem started again. I tried recovery with no avail. I was adviced to test it by connecting a monitor to determine whether it was the lcd display intermitter. When I try connecting to an external monitor nothing is happening, fn and f7 won’t work either

Please help