This sounds exactly like what happened to me one morning on the way to work. Was it pouring rain too?
I didn't have the brake light on, but the engine light came on. It also started to overheat, and no heat was coming in to the cabin (I was trying to cool it down that way). My first thought was the water pump, but it turned out the fan belt had come off. Don't ask me how! It wasn't broken, just off (but chewed up). It turned out to be quite a difficult thing to get a new one on. I kept thinking the mechanics didn't know the secret Mercedes handshake or something, but from what I read on this board they ARE difficult to get on. YOu have to take the alternator right off. But, at least it's a cheap fix! Good luck...