Cannot install on live Joomla site
Welcome to StackExchange!   There are fewer installations of CiviCRM on Joomla than Drupal or WP, but it does work, and for most of what it does, Civi doesn't care which CMS it sits on.
You may be hitting problems described here with HostGator. In general, I'd only try to run CiviCRM on a hosting provider that explicitly supports CiviCRM.
The end of the error message simply says &quot;DB Error: unknown error&quot; - which is not much use to you or us!  Do your log files provide any more information about the error?
If the logs don't provide further info you could try connecting to the db directly (either command line or phpmyadmin) and copy/paste in the create table statement and see what error it gives.