I wonder if every st16 is shipped with the power button on... That's how I received mine. No issues after charging it up. It appeared to be shut down even though the power switch was on so it must auto power off. The battery was at about 25%. It took a while to charge but has not caused me any issues whatsoever. It holds a charge fine. I wouldn't worry about it.
@Digital32, terrible way to start, huh. Follow SoCal's advice, be warned that it takes a long time to charge the ST16 battery. To check progress, every hour or so, touch the screen with your finger. A display should appear, showing a rough idea of the charging progress.
Who did you buy the H from and are you in the USA? If the ST16 will not respond at all after several hours, just stop and contact the seller, or Yuneec. Yuneec USA is often available on Saturdays by phone, do not email. Kindly let us know if you still have problems.