There are many posts on this type of problem with Sony Vaio laptops. Solutions vary from removing the CMOS battery to reset the BIOS, to removing the main battery, to swapping memory modules and other solutions - some worked some failed.
I suggest the first thing to do is connect the laptop to an external monitor and see if you get graphics. If so it may be the screen has failed but a visit to your nearest repairer is likely to be your best bet. Unless others more knowledgeable than I am can come up with better ideas.