I have a generation 1 IPad, having trouble coming on after charge.

I have a generation 1 IPad, everytime the kids let it die I have trouble getting it to start back up. I charge it for hours and when I come back to it the low battery image comes up. If I unplug it the needs charged image comes up. This has been going on for the passed six to ten months. I have been able to keep trying both pluged in and unpluged to get it to come on. I try just the power button, both power and home for 30 sec. plug it in to the computer and do it. everytime I have been able to get it to come on. When it does come on it is fully charged. It runs great for a Gen 1 that is 3 years old. I tell the kids to make sure they are charging it and not lettting it die, but they are kids. So again today I have a die IPad and everything I try is not working. Any ideas on how I can get this thing to work and maybe not have to go through this again.