The story I heard was that it was a very very hot day. The nose wheel sank into the soft tarmac while waiting for line up clearance. Because the pilot couldn't move the aircaraft with loads of power on, he assumed the brakes must be binding. This turned out to be a red herring and confused the engineers and others who came to help, and who didn't immediately spot the ridges/chocks of tarmac infront and behind the nosegear - all the attention was on the mainwheel brakes. Eventually it was realised that it was the tarmac that was to blame.
As for planes with nosewheel brakes - the B727 that I used to fly had them.