I have a vaio model PCG 792L and when I press power switch the lights power as if going to turn but screen remains black, laptop does not turn on.

You need to get it to a hardware store that does repairs. That there is the connection cable from the laptop part to the monitor part being either loose or broken.

Try here: http://esupport.sony.com/US/p/model-find.pl?mdl=%20pcg-792L&PRODTYPE=32,33,63,71,118,7,102,26,80,119,72,125,44,55,27,74,84,57,61,108,115,109,103,89,113,35,78,48,77,106,29,123,50,39,64,114,12,41,58,52,81,60,45,66,73,101,76,86,62,54,67,70,68,2,17,1,88,116,100,82,110,25,28,120,83,59,69,112,49,24,104,124,53,122,79,121,42,46,13,105,126,6,85,3,36,9,51,111,47,38,4,34,37,43,117,5

Yes you can reinstal the OS!

if you want i can give you service manual

Have yo tried going into power settings and adjusting them so that full power stays on for longer period before sleep/hibernation mode activates

try this take a flashlight on look at the screen it will be hard to see but if you see your screen their is a connecter between the screen and the top of the laptop that is hard to see but you can take a pen must be steel and put it between the screen and laptop and your screen should come on if not them you will need a new screen but i know it works i did to laptop

Try control panel and double click the mouse icon then settings you can adjust sensitivity there

Try Holding The Screen Up to A Bright Light And Look at it from an angle to see if you can see windows running without the light.... If you can..... The Problem Is Either Your LCD Bulb (needs Replacing) or It's the Power Inverter....

If.. You See No OS Running .. Just Black You Could Need Either A New Display ... or your Video Card/Chip is Shot...
Try Connecting an external Monitor if able to..... If It SHows Up On An External Monitor then Your Video Card/CHip is Good..

If You Get No Display, But The Black Screen Lights Up.... It Is Either The Display Cable Or The Display Panel Itself....

It is probably the inverter. You can get replacement parts here:

http://www.piezas.biz/epages/wwwpiezasbiz.sf/en_GB/?ViewObjectID=56222