My sony vaio powers up, but it has a black screen and cant hear the fa

take the side panel off the case. green power led on case and mb does not mean the ps getting full power. check that the cpu fan is moving and the case fans..put your hand on the hard drive and see if you can feel is spin up.if they are...try the pc on another monitor and try the monitor on another pc or laptop. if the monitor works....you rule out the monitor as an issue.
to see if it power or another part. if the hard drive is spining and the cd-rom and floppy act like the pc is posting. when the power button is pressed. turn off the pc and unplug it from the wall. then pull the video card or ram out. then turn the pc on. if the mb and power supply are fine or working you should get a cmos beep code if the mb has a speaker.
if you dont see the fans moving or they just twitch...then it a power supply issue. if a new supply is installed and it does the same then there a short on the mb or one of the cards. i say short as a part can fail on a pc and cause a short to ground. if the ps turns on you get a smoky pc. most ps can see a dead short and not turn on. as it summer here in the us a power glitch or a close lighting strike can fry a pc. most fried pc not from the power supply but from the cable modem/ethernet port.

Thank you Smorizio, I give it a try.

Arent' all Vaios laptops? If so, some of the steps you won't be able to do.