I am having the same issue. I have completed the event to get the station. I have tried different radios on different surfaces. When my sim is commanded to turn on or listen to "Nature Soundscapes" she will approach the radio and then stop. The icon for the active tasks disappears and the radio does not play. I'm assuming it may be a possible mod conflict. Do you have your mods active when trying to complete the quest?
I helped a friend with the exact same issue.
Go to the sims 4 folder where your saves and mods and every thing is. Go one folder up and rename it to whatever you like. Sims 4 modded does it for me. Then go into the game which wont have your settings and mods for the moment, create a new save, create a simple sim, go into live mode and do the event.
If you need to cheat you can install UI cheats extension without issues. But more mods dont make sense.
After you are done with the event, go to the folder again and now you see the new Sims 4 folder the game created for your new save. Rename it to whatever you like. Sims 4 Event does it for me. Then rename the old folder to Sims 4. Now you have the rewards and your usual game.
Keep the event save folder for the next event.
