I'm having the exact same problem. I've had my Zune for about 6 months, and never had a problem with it until now. I plugged it into an AC adapter, it restarted itself a few times and now the Zune pad won't do anything. I can't even turn the thing off. I'm just going to wait for the battery to die and see if I can do anything upon recharging it. :P
Otherwise, Microsoft's hearing about this.