Alrighty!
So. unfortunately the repair business is a trial and error basis. so i will give you my procedure on diagnosing a samsung tablet.
1) New Cable/Block. Dont assume your accessories are not at fault!
2) External Physical Inspection: Any signs of burns or bubling near the charge port? This is a sign that too much current was pulled from the wall, and can usually give us valuable info on if the charging port needs to be replaced.
3) Internal Physical inspection: Crack open the device, and scan for physical failures. Blown/damaged/missing components, Bloating in the battery, disconnections. Repair these as needed.
4) Check the battery for continuity: Read the voltage levels accross the + and - nodes (Red and Black wires) make sure there is a voltage coming out of the battery. i personally use my Variable amperage Power supply to see if the ciruit connects. if not, Replace.
5) Excite the battery: Use an external Variable Amperage power supply set at 5.5V Force current into the battery at it's corrisponding terminals for 10 minutes. (This bypasses the charging circuit on the board) a lot of the time, a battery will drop below its threshold, and be unable to be read by the motherboard. exciting it will pull the voltage to a proper level, and your board can read it again. plug it in, and see if it charges
6) Try a new Charge port. So! if the above steps dont work out for you, then you will need to replace the components one by one until you fix it. Starting with the charge port, since it is the cheapest purchase, solder a new one on to see if this fixes your issue!
7) New Battery: moving up in cost, the new battery will need to be attempted from here. Even if there IS a circuit in the battery. sometimes it doesnt pump out enough current to boot the board.
8) Board failure: at this point something has gone wrong with the board, and it becomes more expensive to repair than to replace. i would look into buying a new tablet at this point
Regards