An LCD screen cannot produce light. It needs an additional light source.
A Backlight is the additional light source.
A Backlight is a CCFL or a series of LED lights, (For present technology)
The Toshiba Qosmio E15-AV101 uses a CCFL.
Cold Cathode Fluorescent Lamp.
Similar to Fluorescent lighting used in homes, and businesses, but on a MUCH smaller scale.
(Usually 2mm Wide, by close to the height of the LCD screen, Long )
A screen Inverter is used to convert the power (Electricity) of the laptop, for the Backlight, and LCD screen.
90 PERCENT OF THE TIME the fault is the screen Inverter.http://www.pelltechnology.com/Toshiba/Laptop/Toshiba-Portables-Qosmio-E15-Series/AV101/Toshiba-Qosmio-E15-AV101-Backlight-Power-Inverter.html
The front thin plastic frame in front of the LCD screen, is the Display Bezel.
Resembles a picture frame in it's design.
Toshiba's name is Display Mask.
The screen Inverter is located behind the Display Mask, and mounted at an area below the LCD screen.
A) Remove ALL power. Remove the AC adapter (Charger) and Battery.
B) It would be best to buy, and wear an ESD wrist strap. Average cost is around $3 to $6. (Electro Static Discharge}
Connect it's alligator clip to a good ground source.
Your body carries Static electricity. Static WILL fry out (Short Circuit) the delicate hardware components inside a computer. The ESD wrist strap prevents that.
It is arguable that you are just replacing a screen Inverter, and the above is 'over-kill'.
I would rather spend $6, and not have to worry that I could accidentally make my laptop an expensive paperweight, or doorstop.
Use a multi-compartment container for the various screws you will remove. SOME screws look VERY similar to other screws.
DO NOT mix them up.
C) Open the laptop, lay the Display Assembly all the way back. (Down)
Pull up on the right Hinge Cover, and remove it. Do the same for the left Hinge Cover.
To the immediate right of the right Hinge Cover, and immediate left of the left Hinge Cover, are two Philips head screws to remove.
These screw heads are covered by a piece of masking tape.
The tape is carefully removed, (May be able to use it again), and the two screws removed.
The Display Mask is very thin, therefore quite flexible.
The mask has plastic tabs that protrude from the outside edges.
There are matching tabs on the Display Cover.
(Display Cover: Plastic top cover of the laptop. Covers the LCD screen)
The Display Mask tabs snap into the Display Cover.
Go to either the Left side, or Right side of the Display Mask.
Go to the inside middle edge.
Halfway between the top and bottom of the Display Mask, and to the inside edge against the LCD screen.
Use a soft cloth laid on the LCD screen to protect it, and use a finger to gently start lifting on the middle/inside edge of the Display Mask.
(Cloth is to protect LCD screen from your fingernail)
With the Display Mask lifted in the middle, the width of a fingertip, ease another finger beside it. Start moving away from the first finger, and lifting up on the Display Mask.
The tabs of the Display Mask will start 'popping' out of the Display Cover.
Go around to the top of the Display Mask, and head towards the opposite side.
Once the Display Mask is halfway popped loose, the rest of the mask should come free.
Note that you have to slide the mask over to the Left, to clear the Latch, when removing the mask.
You will now see the screen Inverter,mounted to an area at the bottom of the LCD screen.
Unplug the cables from the Left, and Right side of the screen Inverter.
Note that the connectors on the cables are different, and can't be mixed up, as to where they plug in.
Remove the single Philips head screw from the bottom/middle of the screen Inverter.
Test the screen Inverter before removing;
This requires a sensitive (Read fairly expensive) multimeter,http://www.fonerbooks.com/test.htm
A) Low Cost,
B) Ease of access,
C) No tool available to test,
D) 90 percent of the time the fault is the Inverter,
the screen Inverter is usually replaced by the consumer.
If the screen Inverter proves to Not be the problem;http://www.pelltechnology.com/Toshiba/Laptop/Toshiba-Portables-Qosmio-E15-Series/AV101/Toshiba-Qosmio-E15-AV101-CCFL-Backlight-Bulb-for-LCD.html
Replacing is a procedure that is fairly intensive, even for an experienced tech.
The LCD screen (Toshiba = LCD Module) is composed of many layers.
These layers are set in a specific pattern by the factory.
The layers are held in place by a Screen Frame. A thin metal frame that resembles a picture frame. (Toshiba = P-Chassis )
Part of the screen frame is removed. The screen frame Bezel.
[ The P-Chassis, or screen frame, is composed of TWO parts. The lower main half which is the P-Chassis, and a thin upper half which is the screen frame Bezel, or P-Chassis Bezel.
This will all make more sense when you view it in the Service Manual, on Page 281 ]
Anti-Static computer gloves are usually worn to prevent soiling the LCD Panel, (LCD screen)
(Soiling = Oil from your fingers, dirt, and also helps prevent scratching the LCD screen )
There is a panel, or Board, that goes across the top. Three screws are removed. Then open the bent portion of the TCP of the board, and remove the Backlight.
The Display Assembly needs to be removed from the laptop, in order to perform replacing the Backlight lamp. (Bulb)
Service Manual link to be included in a Comment, along with more pictorial information.