If you did an upgrade of an 10.10 install where everything still worked fine (and where the Apple-supplied java 6 runtime was installed), the following solution might work. I had the same problem as you had, and this solved my issues:
- Quit IntelliJ and go to the Applications-folder in Finder
- Right-click the IntelliJ.app and choose: Show package contents
- Open the Contents-folder (this was the only file/folder in my case)
- Open the Info.plist file using a text-editor of some kind (TextEditor should do the job, but I prefer using Sublime for such tasks).
Find the following tag:
1.6*, from the string-tag, so it becomes:
- Save the file, and try to start IntelliJ again.
As I said, this seems to work for me. I do have to note that I am using IntelliJ 14, but I think this process should work for 13 as well.
Also, when a more permanent solution from Apple comes out, it might be a good idea to undo these steps (just add the removed text again) or reinstall IntelliJ completely.