First, let’s attempt resolving this issue with your Apple device by trying a hard reset, then proceed from there if that does not resolve the problem:
Disconnect the device from it's cord, if plugged in.
Press and hold your Sleep/Wake button (on the top) and Home button (on the front) together for around 10 seconds.
When the Apple logo appears, release both buttons.
The next thing you should see after the Apple logo is the home screen a few minutes later.
If the above does not work, plug it straight into a power outlet and try again.
If you hold down those two buttons for long enough then the screen should indeed eventually go black and restart. Do you see that and it's just returning to the Apple logo or can you not get it to restart at all?
can you tell me how you normally back up this iPad? Via iTunes or with iCloud?
Make sure you have downloaded and installed the latest version of iTunes on your computer before attempting this:
(Mac users can run System Preferences > Software Update (or “Apple Store” for OS X 10.9 users) > Check now to get the latest version for their system in most cases.)
Disconnect all cables from your Apple device.
Open iTunes on the computer
Turn off the device (press the sleep/wake button on the top until the device simply shuts off, if locked up).
Press and hold the Home button. While holding the Home button, connect your device to the computer running iTunes. (If your device doesn't turn on automatically, turn it on.)
Continue holding the Home button until you see the Connect to iTunes screen.
iTunes will alert you that it has detected a device in recovery mode. Click OK, then restore the device.
It may ask whether you wish to restore a backup from iTunes or from iCloud. You should use iCloud in this case, which should have the latest backup of your personal data.
That's fine, just follow the link and download the latest iTunes to your Windows computer as normal.
Great, if you haven't installed it yet, please do so and run it. Then answer any set up questions it may ask (defaults are fine).
Disconnect all cables from your Apple iPad.
Turn off the iPad (press the sleep/wake button on the top until the device simply shuts off).
You should see an iTunes icon on your desktop or among your other programs.
Use the charging cord to connect the iPad to your computer. The end that plugs into the power adapter is a normal USB connector.
Is this the cord that came with your iPad as new? if so then the end of that cord does indeed pull out of the square power adapter that plugs into the wall.
Ok, I understand.
You can reply back after you get the cord and I will respond as soon as I come back online for work tomorrow.
Here are the directions again. Go through them step by step and let me know where you have any problems.
As long as iTunes is running, it should matter what screen it is on. It should pick up the iPad and move to restore mode.
That's not good in regard to the battery, however, we don't know what it's doing in it's current state either that could be running the battery down as quick as it charges. If there's a physical problem, we should know shortly.