So you're firing up the 'ole Herk and one of the four Allison turbo prop engines won't turn over due to a sheared starter. You've got 2 choices to get things going in the event that a repair is not an option. Both choices are equally awesome.
First option requires another C-130 to preform a buddy start. The prop blast from your buddy allows the dead engine to windmill fast enough to get her started. The obvious limitations here are that a second aircraft needs to be available and both planes have to be operated at an uncomfortably close proximity.
Option 2 requires a long runway, but can be accomplished without the help of a buddy. A 50 knot high speed taxi is an approved method to create enough flow through the dead engine to get the prop windmilling and initiate a start. Here's the Blue Angel's C-130, Fat Albert, performing this maneuver at the NAS JAX airshow this summer after a failed attempt to repair the starter on the #1 engine. As they say, "the show must go on."