The flight instructor (CFI) and student were airborne for about 10 minutes, in straight and level flight, when they heard and felt a “clunk” followed by the sound of the landing gear pump running continuously. They attempted to lower the landing gear and it did not come down. They subsequently smelled a burning odor, which was assessed to be from the landing gear pump, so they pulled the landing gear circuit breaker. They followed the landing gear manual extension checklist and troubleshot the problem, but there was no pressure in the manual pump and the landing gear would not extend. The CFI then performed a low pass over the runway and tower personnel advised that the nose gear appeared down and both main landing gear appeared partially extended. The CFI then performed a gear up landing during which the left main landing gear collapsed, resulting in substantial damage to the left horizontal stabilizer spars and the rear bulkhead. The CFI surmised that the right main landing gear locked down during the flare. The wreckage was examined, and the nose gear up hydraulic line was found failed. The line had separated from the compression fitting on one end, which resulted in a loss of hydraulic fluid. The manual pump in the landing gear system utilizes the same landing gear hydraulics as the normal extension system, so the loss of hydraulic fluid rendered it inoperable and made it unlikely for all the landing gear to extend and lock down. The failed hydraulic line was installed in the airplane in May, 1993, and had 6,776.2 total hours since installation. The failed hydraulic line was replaced, the airplane was placed on jacks, and the landing gear was swung and functionally tested using both the normal extension/retraction procedures and the manual/emergency extension procedures. The gear operated normally with each procedure and no additional failures or leaks were noted.