There are several things to consider here-
1. The video could be dead, and you're just not hearing anything. Take the laptop to a computer monitor, then use the function key and the key with the monitor symbol on it. See if you can function the display to the monitor.
2. The motherboard and/or cpu could be dead. Do you see HDD led's on the Vaio to indicate any sort of activity? If the led's are there and not doing anything, that's not a good sign. And those parts suck to replace, they're expensive, and frequently hard to order yourself, the manufacturers keep those parts for their lacky techs to order under a login website yadda yadda.
3. If your laptop is under warranty OPENING IT YOURSELF, IN ANY WAY, WILL INVALIDATE THAT WARRANTY!
4. Try removing your battery, hooking the Vaio straight to the power outlet. Try booting now. Most laptops won't act stupid after a battery goes bad, but hey, it's worth a try.
5. Can you verify the laptop has ever worked? If not, I'd take it back to where you got it. If so.. can you describe a little more of the details around the "death" of the laptop? Operating System and hardware details, model numbers, etc. would be helpful.
btw- Welcome to Techspot! :wave: