The captain said he was asked to expedite the takeoff because of traffic on short final, so he advanced the throttles to partial power to make a rolling takeoff. The aircraft's nose wheel crossed the centerline of the runway to the right, and the captain corrected back with nose wheel steering to the left. As the nosewheel reached the center line, he tried to turn the nose wheel back to the right, but the aircraft did not seem to respond and the nose continued to the left. The aircraft's speed was increasing and the power was still set. The captain placed both hands on the nose wheel steering, but it would not move. He then ordered the first officer to reduce power. The captain then applied full right rudder and braking but was unable to stop the aircraft before it left the runway. When the aircraft was ferried for an inspection, the co-pilot of that flight stated that the nosewheel steering, brakes, and thrust reversers all operated normally.