I'm glad I found this forum. My 11s is doing the exact same thing. I purchased it about 2 weeks ago, and it had been working perfectly fine until two days ago. The unit will charge up and get a solid blue light. And if I either hit the top button, or use the remote, I will get a singular beep, but the 11s will not leave the base. If I take it off the base, the top button light immediately goes out - as if there is no power to the unit, or the unit is OFF. When I place it back on the charger, the top button will go back to "breathing" orange for a minute, and then solid blue.
The power switch is on,and I toggled it a few times as well. I'll remove the batteries from the remote as suggested in this thread, but to me, it seems as if the power switch isn't functioning, and even if I have it in the ON position, it acts as if it's off.
I'll call customer support later on today. By the way, it would be very helpful if you guys had customer support times in the morning US EST.