Post the manufacturer and model number of the laptop. Model number is located on the bottom of the computer. In the meantime I can only give you a generic diagnosis to follow;
1) Laptop OFF, monitor OFF, connect a VGA monitor to the VGA port on the laptop.
This is an example of a VGA Cable, and VGA connector, (Port),http://en.wikipedia.org/wiki/VGA_connector
(On the laptop near the VGA port it may have RGB, or External VGA, or nothing )
You can use a CRT type of monitor, (Looks like a small TV), or a flat LCD screen monitor that has a VGA cable attached.
2) Turn the monitor on. If a CRT type allow it to warm up.
Turn the laptop on.
By factory default settings, the display should show on the external VGA monitor.
IF not; Hold down on the Fn key, and at the same time tap once on the Display Toggle-Over key.
The Display Toggle-Over key will be one of the F keys at the top of the keyboard. (F1 through F12)
HP laptops for example, usually use the F4 key.
After performing the above, there is no display on the external VGA monitor;
There are at least 3 display options available;
1) Internal monitor of laptop ONLY
2) Internal monitor of laptop AND external VGA monitor
3) External VGA monitor ONLY
Hold the Fn key down again, and tap once more on the Display Toggle-Over key.
NO display shows on the external VGA monitor?
You have a bad graphics chipset, or the mounting of it to the motherboard is bad.
Display shows on external VGA monitor?
You have a problem with the Video Cable, or in the Display Assembly itself.
A) Video Cable:
This cable connects to the motherboard, under the Keyboard area, or just above it.
It then goes along, and up under the left Hinge.
From there it goes up into the Display Assembly, and connects to the back of the LCD screen.
There is also another wire, or two, that comes from the Video Cable, and connects to the screen Inverter
An LCD screen does not produce light by itself. It needs an additional light source. A Backlight is the additional light source.
A Backlight can be a CCFL, (Or two of them), or a series of LED lights.
(These two technologies are used in the present )
A CCFL is a Cold Cathode Fluorescent Lamp.
Similar to Fluorescent lighting used in homes, and businesses, but on a MUCH smaller scale.
[ Average size is 2mm Thick, and the length is almost as long as the LCD screen is in height.
2mm is a little larger than 1/16th of an Inch.
More information on CCFL, and general guide to replacing,http://www.laptoprepair101.com/laptop/2007/12/09/replace-laptop-backlight-ccfl-lamp/
A screen Inverter is used to convert the power from the laptop, for the LCD screen, and Backlight.
90 PERCENT OF THE TIME the fault can be attributed to a bad screen Inverter.
Some average examples of a screen Inverter used in a laptop,http://www.laptopparts101.com/screen-inverter-board/
The thin plastic 'frame' in front of the LCD screen, is a Display Bezel. Has many names, depends on the manufacturer.
The screen Inverter is located behind the Display Bezel, and mounted at the bottom of the LCD screen. (Usually)
Check the video cable connection on the motherboard side, and at the back of the LCD screen.
Just with opening, and closing the laptop, the video cable could have been pinched in the Hinge.
This would lead to the video cable being pulled on, and pulling a connection loose. (Or both connections)
It could also lead to damage of the video cable.
Check the cable's outside sheath for obvious signs of damage.
This may indicate damage to the tiny wires inside.
It is best to completely remove the video cable, and with a multimeter check the wires inside for continuity. (Set the Function knob to Ohms)
B) Display Assembly:
The Display Assembly consists of the;
1) Display Bezel
2) Display Cover. (Top cover of laptop over LCD screen )
3) LCD screen
4) Hinge brackets, and Hinges
5) screen Inverter
7) Web camera (IF installed)
8) Microphone (IF installed in Display Assembly )
9) Screen Frame (Holds the LCD screen assembly together )
If the Video Cable checks out OK, move on to the screen Inverter.
Look to see if the cable (Wires) connections to the screen Inverter are tight.
Physically check, do not assume by just looking.
Is there any obvious signs of damage to the screen Inverter?
To test a screen Inverter requires a sensitive multimeter. Read fairly expensive,http://www.fonerbooks.com/test.htm
Due to the fact;
1) That most do not have a multimeter of this type around,
2) The ease of accessing to replace a screen Inverter,
3) The usually low cost of the screen Inverter,
, the screen Inverter is replaced. Parts changing I know, but you have to use what is available to you.
Replaced screen Inverter, and you still have no display on the laptop's internal monitor?
Replace the LCD screen.
If a laptop uses CCFL for Backlighting, there is going to be a screen Inverter.
If a laptop uses a series of LED lights for a Backlight, there MAY, or MAY NOT be a screen Inverter.
In this case the LCD screen itself is replaced.
If you post the laptop manufacturer, and Model Number, (In a Comment), I may be able to link you a Service Manual. Also there may be pictorials with disassembly information.
Guide you as if I was sitting next to you.