The most likely problem here is a poor connection between the battery and the logic board, or bad new battery. The behavior you're describing is how an iPad 3 responds when it is not well seated on the battery.
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***iFixit Staff Edit:*** For more details on how to diagnose boot issues with an iPad check out our [link|https://www.ifixit.com/Wiki/iPad_Stuck_on_Apple_Logo|iPad Stuck on Apple Logo|new_window=true] troubleshooting page. It contains more information on why this sort of behavior occurs and further steps to fix this issue!
The most likely problem here is a poor connection between the battery and the logic board, or bad new battery. The behavior you're describing is how an iPad 3 responds when it is not well seated on the battery.