During a flight to prepare the student for a CFI check ride, both the student and the CFI could not obtain a green light confirming the nose gear was down and locked. After numerous attempts to assure it was down and locked, the aircraft was landed at Andrews AFB. The nose gear collapsed on landing and the aircraft slid off the left side of the runway. Examination revealed a skewed wear pattern deep within the slot of the nose gear aligner guide. The entire slot was found twisted in a direction consistent with deformation at its upper end of one of the guide walls. The exterior surface of the slot wall which contained the deformation at its upper end revealed marks consistent with short term contact with the alignment bushing which normally rides within the slot. If the bushing did not align with its guide during retraction and bent one of the guide walls, it may cause the gear to fail to fully extend.