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Thank you for reaching out here in the Community.
The way local files work has changed recently. The synchronization between files from PC and your mobile devices over the network is no longer available. The audio files that you want to play within the Desktop app, need to be physically present on your computer's storage in order to be played by Spotify. You have to upload them.
In case you already uploaded them correctly and you're still unable to play them, it will be a good idea to remove all the local files you've uploaded on the app and try downloading them again. Moreover, it might be good to create new folders with the files.
Keep in mind that Spotify supports .mp3, .mp4, and .m4p files. It doesn’t support .mp4 files that contain video, or the iTunes lossless format (M4A). With that being said, some of your tracks may be protected in restricted formats and that might be the reason why they cannot be played.
We'd recommend to head also to this FAQ under "Local File not playing?" to double check if those files meet the requirements listed there.
Hope this helps. If anything else comes up, the Community will be here for you.