I thought my GPU fan had busted too because of the same thing.
The fan runs at high speed when you first start the computer, hence the noise. The fan slows down when the driver software starts up in windows. The Fan is temperature controlled and the speed is controlled by the driver software.
So all is fine and you might see the fan speed up as the GPU works harder.
EDIT:
Just re-read your post. Mine was after installed my new Graphics Card. You've had yours for a while and it's only just happened. Still might be the case though.