What is the history of the iPad before you got it? Was it water damaged or did it suffer strong impacts. Those are things that could cause logic board damage.
There could be a problem with the charging circuit (U2) but it is tough to say since you don't know if the battery you put in there is in good condition. Check the battery with a multimeter to insure it has the proper voltage (it should be around 3.7V). If you have access to the schematics, you need to check if the battery voltage is getting to the logic board.
Beyond that, depending on your experience troubleshooting logic boards, you may need to find a qualified repair shop that does micro-soldering repairs for a proper diagnostic.