-Try to remove and reinstall spotify app on ps3 -Make sure you have defined a name for your ps3 system in [system settings] -> [system name]. After you change system name you will probably have to reboot ps3 before Spotify app works at all.
If neither of these ideas help, id look into network settings. You must have a proper router for your LAN and Wifi to work correctly, as mobile hotspots wont work. Make sure you are using automatic network settings for your ps3, as they should be fine.