I was having an issue where, not only could I not get the speaker to power on, but when placing it on the adapter (to resolve 'protection mode' issue) the speaker chimed the sound indicating charging, but no LED lights would illuminate to indicate that it was in fact charging. It would chime again when removed from the adapter, but would not turn on either way.
I fixed it by doing a hard reset as recommended by BOSE troubleshooting:
Hold mute button for 5 seconds (if successful, LEDs will flash- mine did)>Press power button to turn on.
Note: Bose advises you may have to re-pair devices after performing this reset. This was not necessary for me.
Hope this helps!