Had this problem for the first time just the other day. Before leaving for work in the morning, I had powered it off with just under 50% battery remaining...later that evening it would not power back on.
As it turns out, the battery was dead.
When it wouldn't power on (no matter how long I held power button), I plugged it in. At first was alarmed because normally if the tablet is turned off, when I plug it in the screen will brighten, and a charging battery icon will appear for a seconds before the screen goes black again. This did not happen. After a few minutes (of panic), it started to show a strange white battery icon every few seconds when I had the power button depressed, but it still would not power on. (Keep in mind, at this point I'm assuming the battery has a charge, since it had ~50% when I shut it down hours before). Then, about 5 minutes after that, I saw the screen light up and show the *normal* charging icon. At this point, my tablet was able to power back on, but when it came up, battery was at 1%.
A few things:
1. Apparently if the battery is completely dead, it will take a few minutes to get enough charge to power on, even if plugged in.
2. I'm not sure how my battery went from 50% to 0% in about 12 hours while turned off. I checked battery monitor widget, and it stopped logging events at the same time in the morning that I shut it down (so I know I wasn't crazy and that I had INDEED shut it down). I figure that either the shutdown process went haywire and a process kept running until the device just died, or my battery isn't calibrated correctly to the device and the actual power level of the battery when I shut it down was much lower than the % meter on the device indicated.
3. I've had my battery run well below the 50% mark in the past without any issues, making me think it may be the former.
4. I hope it doesn't do it again. SCARY!
tl/dr: If this happens to you, plug it in for a few minutes before you start to really panic.