Clutch burnt out

you might need to replace the backlight on the screen, the CCFL has burnt up like normal fluorescent light does after a few years of continuous use.
Lenovo Tablet Repair

(this is all i could find on the internet so this is not to say it will help you but try it and see what happens).........PRess the power button and the volume down button at the same time and hold until the unit restarts... it resets the charging cycle and the note will charge reasonably quick from then on... I do this on occasion when my battery seems to charge slow.
plus some people are saying get a new charger.

Submerge your tablet in a bathtub full of warm water. And let sit for about 5 mins. And then try to charge it. Tt should fix your problem. And future reference, the tablet needs to be wet before u microwave it. Otherwise it jusr fries

It charges via USB. Connect it to a computer.

Make sure you're using the factory charger (most tablets require 2.1 amps, or 2100mA.) If that isn't the problem, you'll need to get someone to look at (or test) the battery.

If you see bulging, or smell burnt plastic, you'll need a professional to look at it.

Color lights have burnt out. Replace the screen or get a new tablet. I reccomend an iPad because Android Tablets are weak.

Have you tried resetting it also the fuse or resistor for the backlight might just need replaced

is there any light emitting from the device at all? (turn off light and see if the screen is showing light)

if it is, check your brightness settings on the device

if there is no light it is possible that the backlight burnt out, or that there are settings that need to be adjusted on the device. It is also possible that you downloaded an app that doesnt work properly with your device.

if none of this seems to be whats wrong, more information would be nice:

1) what model of tablet are you using?
2) what version of android OS?
3) what app were you trying to install?

From there you'll be able to get more help if needed.

Call the Fujitsu service 800 number, you may still be under warranty.
It sounds like the inverter has burnt out, take it to a Fujitsu authorized repair shop, your tablet has a security feature that will lock you out if it is opened by an unauthorized repair shop or anyone else for that matter.
They take your tablet security very serious.

Not easy to say what it caused it, but if its bad the problem will be solved whit replacing it.

To be sure you can always run a memtest, download the program version from the site below, burnt it on a cd, reboot from your cd-driver and let memtest check your memorysticks.

http://www.memtest86.com/