There is a way to run and debug protractor web-tests in WebStorm. I just want to share this answer here
Like some of the other responses here, I found that I could run in release but couldn't run in Debug and it would just hang at some point. I found that I had the conf file set to target two browsers and it seems that this was too much for the debugger and it would hang without any more info. Targeting only a single browser fixed this issue for me.