I want know how to find damages on screwing stud. While screwing the back cover, It may cause damage. In that case how i will find damages.

Do you mean the scree will not attach to the back cover anymore? Apparently you have damaged the screw anchor which is embedded into the back cover. When it happens, you’ll have to replace the back cover.

I have a problem with my laptop , it’s refusing to start , I mean when I click on the power button the monitor is blank, it’s not working at all , only the wireless and another lights are flashing ! My laptop is Sony Vaio VGN-CR23G

It’s hard to tell what’s going on without looking at the laptop. Could be memory failure.
Do you have two memory modules installed? Test the laptop with each memory module separately.
The laptop might start properly when the bad memory module removed.

I was recently playing a game on my Sony VAIO VGN-FZ21S when it suddenly cut out without any smell. After it would not do anything at all weather plugged in or not. I then used my multimeter to test the power outlet on the AC adapter and it was 19.5v. I then opened the laptop to bare motherboard level to see what was happening, when I decided to test the AC adapter again, suddenly it worked. I reassembled it again and now it works 100%. My question is why would it act like that?

Not sure what’s causing that but I had exactly the same problem with one of my Sony laptop two or three times.
The laptop shut down without any reason but after I unplug the AC adapter and reconnected the battery it started properly.

Also, this could be related to CPU overheating. If CPU overheats, the laptop will not turn on until the CPU cools down. Make sure the heatsink is clean. If it has much dust inside, clean up the heatsink with compressed air.