Jena, this is a new one on me. Normally the lack of a Play button indicates the media either didn't upload or isn't properly linked to your page. Here, the text and button show up as soon as you click on the calender! Have you set it to "hidden"?
I'll remind you now ... you only have 30 days to configure your page, unless you go Pro. So, if "Give it a listen" isn't the line you want, you should change it soonest. "Time keeps tickin", so to speak.

Oh, and another point. Anyone can access your podcast by clicking on the View Podcast link beside your name.
Dave M