One problem related to power steering light on has been reported for the 2005 Mini Cooper S. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2005 Mini Cooper S based on all problems reported for the 2005 Cooper S.
Found need more turning of steering wheel at traffic light into the cross street, then parked the car, turned off engine but still found something running in engine bay. Thought it was the fan to cool the engine off, so didn't pay attention. At lunch, come back to pick up the car, and found its battery was drained almost totally. Jumped the car without issue and drove back home without issue. Turned off engine and still hear the noise of something running in the engine bay. Pulled all fuses to see if can identify the problem, doesn't help, something still run with load noise. Searched internet, found other owners also experienced the same and is the power steering pump failure, some even found failure while driving.