What adapter are you using? http://support.apple.com/kb/HT4060
And your new iPad might be iPad Mini? iPad mini and your iPad 3 has it's own charger and I don't think one charger adapter can charge different devices.
If this isn't your answer , you maybe need a battery replacement! Make an appointment and take it to the Apple Store.
If it's your iPad problem , you might want to make an appointment and take it to the Apple Store to give you a new iPad3
Does the iPad make the little "plink" sound when you plug in the charging cable? Has is worked previously? If you are using the new lightning cable, I have found that sometimes is doesn't take, and I have to remove it and plug it in again. Sometimes flipping it over works, thought it's supposed to work either way. I think the new cables are a little flaky.