A bad battery is the typical issue for these kinds of symptoms. However, after trying two different batteries, it may not be the case here. To know for certain, measure the voltage of the battery directly (while removed from the iPad) with a multimeter. If you are measuring more than 3.5V, the the device should boot fine.
If the voltage looks good, then you may have damaged something when you disassembled the iPad. Check the logic board in the connector area and inspect the flex cables for tears, even tiny ones.