Player needs JavaScript and Flash turned on.

Where do I turn on JavaScript and Flash? When I go to my sermon page this error is there, I can play sermons by clicking in to them but on the main page this error exists. I can't find where to turn the options on

That would be in your browser. But since it works in the sermon detailpage it is likely some JavaScript error on the site which prevents the player to load.
You can have a look at your browser console window, or if you tell me the URL of your site I can have a look myself.

The site KinnairdPark.com
If you want login credentials to the admin end I can set you up and pm them to you.
Thanks

The PixelOut player you have there doesn't support playlists.
You need another player at least for the list parts (eg the JW Player one). Or just disable the player for the lists.

I have tried using the JW player, but it says it needs a key. I have gone to their website to get one but can't find where to obtain one.

I think you can't get a free key anymore for a self-hosted player. You would need to use the cloud based one or pay them for the self-hosted.
Once logged in you get to dashboard.jwplayer.com/ and there on the left hand side is a menuitem "players". There you can create and customise a player of your liking and use the "Cloud-Hosted Player Library" URL in the plugin. Imho it should also work with the JW Player 8.