I got my (7" tab 3) tablet back today from Samsung--warranty deemed void because I removed the back cover. After hours of desperate, last-ditch strategies and button-mashing, I got it to turn back on normally. Here's what I did:
1) Remove the back cover of your UNPLUGGED tablet. (Youtube has good tutorial videos. This will void your warranty.)
2) Disconnect the battery (small wires leading to a tiny rectangle at the bottom of the board).
3) While the battery is disconnected, PLUG IN the tablet.
4) Reconnect the battery (I felt mine "snap" twice into place).
5) Turn on the tablet (mine came on immediately after I pressed the power button).
I haven't seen a tip like this on other forums, but it's worth a try if nothing else is working for you. Cheers.