What happened to the iPad in the days or weeks leading up to the issue; was it dropped, repaired or came into contact with water?
My first thought was a bad battery as well but if you have already installed a replacement battery and have the exact same issue, then your problem is probably elsewhere (it could still be a bad replacement battery…). If you already have a backup of the data, you could try a DFU Restore of the device. This would solve any software related issues.
If that doesn’t help, then you likely have a hardware issue, either modular in nature or on the logic board. You could try to disconnect the LCD and Digitizer, the cameras and buttons etc to see if the logic board and battery alone will allow the phone to boot into iTunes. Beyond that, you will need to have this iPad looked at by an experienced micro-solderer.
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