Look closely at your battery connector inside the iPad (or don't, because you can live with this problem). You will see that you have accidentally flicked off a tiny component at the battery connector. This component is necessary for the battery to communicate its 'gas gauge' to the logic board. Without it, the iPad will charge and discharge just fine---it will just never move its percentage. Despite whatever percentage the iPad shows, if the real percentage drops below 1%, you will get a boot loop phenomenon....the iPad won't 'know' to prompt you to plug it in, so it will continue to attempt to boot with no battery.
You can live with this, and just make sure to charge the battery regularly.
Or of course, your problem could be something else entirely....but I betcha I'm right :)
jessa