I get a message that my computer is not authorized to play a song that I purchased. I authorized and received a message that my computer is authorized but when I try to play the song, I get the same message that my computer is not authorized.

Repeated requests to authorize an already authorized computer for store downloads typically indicates you have corrupt or incomplete copies. Delete the tracks that won't play from your library without hiding from your purchase history. Redownload using the cloud links that should remain, or close iTunes and reopen if they don't show up straight away. While downloading click the activity widget and turn off the option that allows for simultaneous downloads.

If that hasn't helped see If iTunes for Windows prompts you to authorize your computer when you try to play purchases - Apple Support.

tt2

Most people only have content from one account which keeps things simple. You can select a problem track, press ctrl+i to get song info, and look at the File tab to which account was used to purchase it. See Authorization vs. association - Apple Community for background and details on the complications that can arise if you want to access past purchases from more than one account.

tt2

Ive transferred my music and data from previous device but my MacBook won't play them it says their not authorised go to account and authorise but can't find where to do this

doesn't say what account to go to or anywhere that authorises playing of my purchases on my apple account

Neither of these things fixes this problem. For some reason, the permissions from Audible never make it to Books. Very frustrating!