I've been having an issue recently where the web player, using firefox, will simply stop working. I get a little popup about how 'a tab is slowing down your browser' and I've got to kill it if I want to resume listening. This issue has been occuring since the same update in which the (now mostly fixed) playlist loading issue was introduced, and is extremely frustrating.
Could you find out if your Firefox browser is up-to-date? If it is, there might be a setting preventing you from listening to music on Spotify. Check the firewall inside Firefox to see if Spotify is blocked. You could also choose to restore your Firefox preferences back to default.
Alternatively you could use any other of the following 4 web-browser which are supported: