I installed PHPStorm as a standalone software (meaning I just downloaded it and started the program via terminal in bin folder).
While it was open I clicked on the sidebar (rightclick->save to favorites) so I can start it from there (this was working).
Then I realized that it was the wrong version, I wanted to download the EAP version. So I deinstalled it, simply by removing the JetBeans config directory as explained here. Then I downloaded the EAP version, removed the old favicon and created a new one.
The problem is, the new favicon still starts the old application. Now I removed also the downloaded folder of the old PHPStorm application. Now nothing happens when I click on the favicon.