You can try deleting the ~/Library/Application Support/Spine/ directory. You may need to reach the directory by using cmd+shift+G in Finder. The directory contains preferences and update files for Spine. Deleting it will cause Spine to use the default settings and to download a new update.
Since Spine appears to start successfully, I'm at a loss as to what could be the issue. If you are somewhat tech savvy, you can download a 64-bit JDK, find the PID of the Spine process that isn't responding, then run the jstack tool from the JDK using that PID. This will dump a bunch of data which you can pose here or email to contact@esotericsoftware.com.
Sorry you are having such trouble!
