My first thought was that the wall adapter had failed. From your testing, however, it sounds like this isn't the case - but you might try testing this wall adapter (and the USB cable) with your phone or some other USB-powered device, just to be sure.
Failing that, it may be that the ICS itself has had a component failure. Contact Intel Customer Support directly (via phone or chat) and make arrangements for a replacement unit to be sent to you...
Thank you for your response!
In the meantime I tested out the AC-adapter with my smartphone and it worked flawlessly!
Tomorrow I will contact Intel Customer Service by phone. If that does not work out, I will contact them by mail. If it gets sorted out, I will update my OP.