`tor` performs many checks before starting, stopping if something in your system is deemed insecure. For example, wrong owner or bad permissions on `torrc` file could be the cause. A similar check is performed on `tor` executable itself.
You should run `tor` in a terminal, and check its output for errors. They are quite verbose and easy to understand. Fix those errors and `tor` will run.
If you can't be bothered with reading error messages, you can try to navigate to the directory where `tor` resides and execute the following command as `root`:
chown -R root *
Pay attention when executing this command, it may wreck your system if executed in the wrong directory.