A PA34 Instructor pilot reported 'Gear In Transit' light remained illuminated after takeoff; and a fly-by showed a partially retracted nose gear. After landing nose gear collapsed.

Narrative

Gear in Transit light stayed illuminated after gear retraction on initial takeoff. Crew went to practice area to trouble shoot. Crew consulted POH for recommendations. Gear was recycled several times to include manual extensions with various G loadings (up to approximately 2G) and airspeeds of approximately 80 KIAS. All extensions resulted in partial extension of nose gear. A gear check was accomplished by flight school's Chief Instructor who confirmed partial nose gear extension. Emergency was declared with Tower. Aircraft was flown-by Tower who confirmed partial nose gear extension. The door to aircraft was opened before landings to ensure ability to egress aircraft. [Two] attempts were made to bounce the nose gear into place with firm touch and go landings to no avail. Crew elected to full stop aircraft. Upon landing; mixtures were pulled lean; fuel was shut off and master switch was turned off. When nose was lowered the nose gear collapsed and aircraft stopped straight ahead on the runway. Crew egressed as briefed in flight. No injures to personnel.