how can i fix my PCG-8L3L Sony Vaio laptop PCG-GRZ 610?

My laptop will not come on. It will power up but i have no windows or anything shown on the monitor. I have hooked it up to an external monitor and it is still blank and i have tried taking the battery out and unplugging it then trying to turn it on to dicharge the capacitors but no luck there either.I'm thinking it might be the motherboard but do not know for sure. Please help!! Thank-you for any information!