have this problem with 2 of these tablets .
whats happening as far as I can see is that they seem to try and boot up as soon as you plug power in...which is great except when the battery is at 0%, so they start to boot , read that the battery is 0% vibrate and shutdown , which drains whatever power the battery had received by charge , it then starts to get a charge , detects this and then starts up again , and so on ..which means its stuck in a loop that never really gets it enough charge .
What I found worked was to hold volume down and power for about 10 seconds , it'll still try and boot , and fail , but usually this gives it enough charge to start up enough to actually get past the boot screen and start the charging process properly(it'll show a battery at 0% and start charging) .It can take a few goes to get this but it should work .