When selecting a song in any playlist, the song attempts to start but immediately wanders to the next one in the list for a random number of times. The reached song then plays for exactly 9 seconds and then just stops. The 9-second-rule applies to every song played.
First thing you can try is using the Spotify web player in a private/incognito window. This will make sure you avoid issues with your browser's cache. If that doesn't do the trick try again in a different kind of browser.
If this persists after trying another browser, check if you observe the same when connecting to a different network. In case it works with another connection, it's best to contact the service provider of the original network for more information.