My S5 n/a started up right away, held idle, shook a lot, and idled around 5.5k. I noticed that when I tried cranking her again, my starter was completely dead. So my thoughts are the starter is still engaged to the flywheel, even after the engine is on which is why I'm guessing it was idling around 5k. What controls the starter to return and turn off? Is it the spade connection on the starter soleniod? My connections look exactly like the one in the FSM, except I don't know if I have or made the connection to the inhibitor switch. What is that?

If anyone knows how to fix this, please contribute. I would like to drive her once again, this time without any more problems.

 

Sounds like the solenoid (bendex) is sticking. Try tapping it with a hammer. Ultimately though, it will need to be rebuilt/replaced.