The basis of it going green now and then may be something to do with signal. If this is an intermitant issue with your screen then i would check the cable in the back of the LCD.. also the connection on the motherboard.
There are only 4 factors of having bad screen these are
*LCD cable - signal for picture
*Inverter - light for your lcd
*LCD Screen - to view
*GFX Card - produce signal
Hope this helps.