Hello liightfoot,
Thank you for reaching out in Apple Support Communities. We understand you're unable to play Apple Music on your PC, even though you're already signed into your account. We'll be happy to help.
Since you're already signed in with your Apple ID account in iTunes, let's temporarily sign out. Then, sign back in and see if you can play your music without any issues.
If that doesn't help, please temporarily restart your computer in safe mode. Then, restart your PC as normal and test iTunes. If needed, here's how to restart your PC in safe mode: Start your PC in safe mode in Windows
Please let us know if that helps.
Kind regards.