OK, sorry I didn't get to this sooner.
you need to get a test light(or make one), they are cheap.
get the car up in the air.
Hook the alligator clip end to a good ground, like the starter body, a non rusty, non painted part of the engine or something not isolated.
Have someone put the key to "run". Not start, but all the way forward save for start.
touch the small terminal on the starter. The smaller wire, not the big one.
There should be a good voltage there, so the test light should light up as bright or really close to as bright as if is hooked across the battery itself.
Then leave the ground wire alone and poke the larger one. Then tell your assistant to try to crank it and hold it there for a couple of seconds. when the key is in "run" the test light should not be lit at all. When its in "crank" it should be fully brightly lit, just like across the battery.
Report back.
Oh and be careful when you are under there because it might just start on you for shits and giggles.
If both of these light up at the appropriate times, you need a starter. If one or both of them does not light up at the right time, you need to trouble shoot farther up the wiring, all the way to the ignition switch itself and any/everything in between.