Craftsman Lawn tractor 17.5 HP 42" model No. 917.28803 The blades will not engage. The wire is loose at the handle but not broken.

Hi,
Looked up your manual and it does not give the parts breakdown. There is an idler on the deck that is on an arm that the engagement cable connects to. It is extremely likely that the pivot for that idler is rusted or corroded. Taking it apart and cleaning it with sandpaper or buffing it with a buffing wheel will likely solve the problem.
Peace,
Clarke