The Final Verdict:

I did end up changing out my cable (did it in an Autozone parking lot too) and found, alas, that it did not solve my problem. So I went back and bought a rebuilt Duralast starter (cheap, I know, but I'm working in a budget ^_^) and that eventually did get me started. I've been running on the new starter since Friday with no more problems.

The shifting problem went away too, which further leads me to believe my poor starts were pulling my transmission into "limp mode."

Thank you guys so much for all your help. If I ever need to know anything else, I'm glad I know where to go.