When you replaced the battery did you make sure that all the contacts were clean and nothing was bent, etc.? I ask because this can cause it to start and stop. And did you replace it with an OEM battery or an after market one? If it is after market, it is completely possible that it won't work correctly with your device. If that is the case, I would get my money back and return it.
Also you may want to check the same thing with the charger port. Try a different charger and see if it works.
Lastly, make sure you are trying to charge it with the tablet off, not on.