Are you able to login via the Terminal, as described later in Step 4, also in Step 7.
If so, you can access all the logs in /var/log
For this problem, start with /var/log/horizon/horizon.log
After successfully logging in via the Horizon UI, I see the following log entry in horizon.log:
2015-06-21 15:12:43,259 2432 INFO openstack_auth.forms Login successful for user "admin"
You will likely see some error messages in your version of horizon.log, and hopefully those give some clue as to what is going wrong.
You can similarly find the logs for all openstack components in /var/log/<component-name>