Re: Apple Music trial doesn't work, can't connect
If you have held an Apple Music subscription at any time before, you may not be eligible for the free trial.
Else:
Apple support has a trouble-shooting article online that may be helpful with connecting to Apple Music:
See what to do: If you can't connect to the App Store, iTunes Store, or other Apple services - Apple Support
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Re: "I can even get to the Apple Music page that shows the latest releases they're promoting".
You may need to log-in to Apple Music with your Apple Account details to activate the free trial
See how to: Sign in to your Apple Account in Music on Mac - Apple Support
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Please Note: In order to not be charged for the month after a free trial ends, you need to cancel at least 24 hours before the free trial ends. (You immediately lose access to the free trial)
See: How to cancel Apple Music - Apple Support
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Resource: Apple Music User Guide for Mac - Apple Support
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Apple's Music support website: (info / support / contact options etc.) Music - Official Apple Support