Same with my Galaxy Note 8.0. all of it... charge, black screen, no battery shows up, no green light. I replaced my battery, and charge port myself (for $24 total btw). going to try power button (under $10) and then the motherboard (under $50). worth it to me... considering I paid close to $400 for this tablet, plus since I work on tablets etc it will help me know how to fix in the future.
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=== Update (02/11/2017) ===
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I just wanted to let everyone know... i had the same issue on my n5110. i repair devices... i have replaced the usb port, battery, power button, and motherboard to no avail really. when i do the old battery stand-by of wetting the (in this case) connectors it will turn on for about 10 seconds (the circle logo makes almost a full circle) then shuts off until i wet the connectors again. so may not be getting a solid connection with battery.
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another person said disconnect the battery (and charge cable) and press power to drain excess power from mobo... then plug in battery and turn on. tried it and nothing. i have been researching and testing theories for over 2months now with no luck. my next step will be to find some sort of way to 'bridge' the gap on the battery connector.
Same with my Galaxy Note 8.0. all of it... charge, black screen, no battery shows up, no green light. I replaced my battery, and charge port myself (for $24 total btw). going to try power button (under $10) and then the motherboard (under $50). worth it to me... considering I paid close to $400 for this tablet, plus since I work on tablets etc it will help me know how to fix in the future.