iPad won't charge - logo appears but goes back to no battery sign

Hi,

iPad battery died yesterday and will not charge back up. I have connected it to a power adapter and it brings up the no battery sign and then the apple logo a minute later but then dies again and repeats this over and over. I have tried different chargers.

The iPad is under a year old but has a smashed screen. My 2 year old stood (with bare feet) on the home button end of the iPad. It cracked a little bit in the corner but I didn't get round to having the screen replaced... so the crack has gotten worse and now the power button is unresponsive. Could this be the reason it's not charging?

Thanks

Leah