You are certain it is actually charged? I ask because just plugging it in doesn't always get you the charge. If it was not showing it was charging, then it may not have worked, plugged in or not.
Also, is it the whole tablet that won't turn on, or just the screen won't?
Try holding down the power button for about 20-30 seconds and see if it will turn on then.
You should make sure there is nothing in the plug (the part that goes into the device, on the cord) or in the devices port. Dust, lint, dirt, etc., can get into it and then it can cause you not to get a connection that will work right.
There could also be a problem with the charger, the charger port and/or the battery itself.
First you need to make sure the charger cord...