Remote control not working with reset Apple TV (black model)

Today my Apple TV remote control (the thin, silver one) suddenly stopped working with my Apple TV (black model). If I press the menu button the "bong" sound plays ok, but no other button makes any reaction.

The remote app on my iPad2 did work, however, so I used the remote app to totally reset my Apple TV, hoping that this would solve the problem.

Now the Apple TV starts up and shows the initial "Select language" screen, but still the remote control does not work, and because of the reset procedure the iPad2 has no connection to the Apple TV anymore.

Tried to hold down MENU and "left" ring on the remote control for 6 seconds, but nothing happens. Tried to replace battery, but same result - don't think the battery is the problem.

Observation: When I insert the battery into the remote control while the Apple TV is turned on, the white LED on the Apple TV immediately turns off. Hence the remote control must be transmitting something. The LED stays off until I press the MENU button on the remote control. Then the white LED turns on again and stays on. But still the remote control does not work with my Apple TV.

It is the original remote control that has always worked with the device.

Now, what do I do???