|Could be the backlight/invertor cutting out (depends if it's pre LED backlit). Could be the graphics chip.|
If you can see a dark, faint display on the screen, then it seems it may be the backlight.
Does it maybe flash back on if you tap lightly at the back of the keyboard, near the bottom of the screen, or on the plastic bezel at the bottom of the screen (DON'T TAP THE SCREEN ITSELF)?
How 'bout toggling the Fn and designated screen on/off key (F8 ?)
As a process of elimination, via the VGA (HDMI if fitted) sockets, try plugging the laptop into an external monitor or TV. If the display shows up, then the graphics chip is ok.
If it's a backlight prob, then it could the light itself, the invertor (if pre-LED backlit), or hopefully just a plug worked loose.
See how the elimination process goes...
You need to be pretty careful/confident to strip it down to check. Otherwise could be a job for your local PC guy.
Service manual for the CQ45, here, may give an indication in there of dismantling procedures.