Did you install is as a service using APT or YUM, or just by downloading the files directly? And how did you try to start Elastic, again as a service, or just by running the binary file directly?
Reason I ask is because the when installed as a service, but then starting manually, you need to tell Elastic where the path is like this:
sudo -u elasticsearch bin/elasticsearch -Des.path.conf=/etc/elasticsearch
Otherwise, you get the error about not being able to file the logging.yml file.
The actual reason Elastic won't start is probably very different, but until it can log the error correctly, you're shooting in the dark.