It is possible that your digitizer ribbon cable connector has come loose, or was not properly plugged back in at the time you reassembled your Kindle. This is a common problem because of the poor layout and design of the cable assemblies.
If the digitizer is disconnected, then the LCD will come on when you press power, but it will go off a few seconds later since you will not be able to swipe the screen to 'unlock' the device from the power on screen.
The solution would be to reopen the Kindle (i.e., remove the back cover) and properly re-seat the digitizer ribbon cable plug. This is the plug on the end of the long narrow ribbon which is folded over and held down by the mid-frame chassis.
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