|Please let me clarify your question.|
On your laptop when you turn on the computer, there is no video or backlight to your LCD, There is no disk activity shown by your activity LED, There is disc activity from your optical drive when you put in a DVD. But your power LED is on.
I have no idea how your system file checker fits into this. Unless you ran SFC before the system crashed, in that case you knew something was going wrong with your computer in the first place. Maybe corrupted files?
You need to start troubleshooting.
The first step is going to be to reseat your RAM. So turn off your computer, remove the battery and power, flip it over and remove the memory cover. Now remove both sticks of RAM and just install one back in. Now plug the computer in and try to turn it on. If that doesn't work try the other stick. If that doesn't work, leave one stick in the computer and remove the hard drive. Now power it on and see if you get anything on your LCD.
If that doesn't work, unplug everything and remove the battery, leave the HDD out and press and hold the power button for 30 seconds, put the battery and the ac back in and see if it post.
If that fails, get a flashlight and shine it on the LCD and see if you can see anything on the LCD.
That should be enough to get you started. So report back here when you are done.
Also Please leave the Make and Model of your laptop.