Support for SermonSpeaker 4.x is canceled as it is for Joomla 2.5. I will gladly assist you with minor issues but I will not fix any bugs anymore in this releases.
The fix is to upgrade to SermonSpeaker 5.x and Joomla 3.x, which is better anyway.
How can I make the sermon "hit counter" move when simply listening to the sermon from the main page and not actually going to the detail page?
I have the option of Title Link Function set to Control the Player because I don't want them to have to go to another place just to click the play button.
However, with that set up....the "hit counter" never moves. It ONLY moves if the Title Link Function is set to go to the detail page.
It's a very simple hitcounter based on pageviews. It behaves exactly like you observed.
If you want to track how many times a sermon is actually played, you have to use GoogleAnalytics.