Touch screen not responding to touch

I have an Apple Watch sport, paired with my iPhone 6. A few minutes ago I raised my arm to check the time, and the watch didn't respond. The screen remained black. I pushed the digital crown and the "enter passcode" screen appeared, but the watch face would not respond to my touch.

When I clicked and held the contacts switch below the digital crown I got the "power off" screen, but the watch didn't respond to my touch. I removed the watch, cleaned the back of the watch and my arm, put the watch on and held both the crown and switch to reboot the watch. The Apple logo appeared, and the watch rebooted.

The time showed, then the passcode screen, but again the watch was unresponsive to my touch. It had all worked just a few minutes ago. I hadn't dropped the watch or hit it; I had just raised my arm to see the time.

I rebooted my iPhone, saw that my watch was still paired, then rebooted the watch. I've rebooted the watch about 7 times now, and still the watch face is unresponsive to my touch. The watch was fully charged last night and lasts all day. I took off the watch, recharged it for a few minutes, put on the watch, rebooted, but still it's unresponsive to my touch.

Now, when I raise my arm nothing happens; the screen remains black. When I press the digital crown, the time shows with a little "lock" icon, but the watch is unresponsive to my downward swipe. In a few seconds the passcode view shows, but I'm unable to enter the passcode. Force touch doesn't change anything.

The watch still shows as paired with my iPhone, but the watch screen is simply unresponsive.

Please help!

Dan