We had the same issue.
First install or update ITunes on to your home computer. Second, attach your IPad via USB to the PC with the latest version of ITunes installed. Third, hold in the IPad Power and Home buttons at the same time until it recycles twice. You should get a screen showing an USB plug going in to ITunes. Fourth, open ITunes, it should detect your device and hopefully let you know there is a Critical Update for your device. Fifth, follow all defaults to initiate update.
I first found pre-boot to ITunes while trying several different methods of resolving the power issue. I was actually first able to charge the IPad by following the ITunes boot process stated above several times. When in ITunes pre-boot it takes a few more minutes longer to fail before powering up. I feel the issue is that the power when down to 2 percent on an old battery isn't enough to survive power usage involved with startup even when attached to a good power source. This causes a continues cycle were as the IPad dies charges to 2 percent, reboots and dies again not allowing for a charge to start. The only regret I have is that I followed previous suggestions and reset my device loosing many photos not yet uploaded to the cloud. I wish the APad would remain turned off when powered off, this would have resolved the issue much quicker.
Such a blasted headache, it amazing how far one will go to avoid paying for repair services. Charges I am sure would have resulted in a battery replacement or even something more costly.