Well, I dunno why the inside appears to be fine when you checked... The Futaba servo you speak of is a standard run servo and doesn't cost anything to replace in its entirety. The problem is that 1. either the little limiter attached to the final output gear has broken off, or 2. the little electrical pot that is attached to the final output gear has unattached itself from the final output gear.

Take the servo completely apart -- again, and re-pack all the gears. Be sure to fit the final output gear (this gear is the one in which the servo horn attaches to) properly to the little electrical pot (an electrical pot is a device with a variable turning radius, much like a guitar volume knob). The final output gear actually sits directly on top of this pot; the pot works in conjunction with the servo motor -- it tells the motor to stop spinning once it reaches the full point in either dorection. I have had this happen many times. Trust me, your problem is exactly this.

P.S. The final output gear is notched so the pot only has one true way to fit. Be sure to center the pot with a pair of needle-nose pliers before attaching the gears. If you don't you will have lots of motion one direction and little the opposite direction.