There are different methods to login to your Hostgator cPanel. Below are the easiest ones.
Login to Hostgator cPanel using Server Name
If you already know the name of your server, just use
https://ServerName:2083 to login to your cPanel.
Using Server IP
If you know the IP address of your server, type
https://Server-IP-Address:2083 to the address bar
Using your Domain name
If you are unaware of the server name or IP address, you can simply visit the
https://domainname.com:2083. You should use HTTPS in order to make this work.
Be sure to replace the 'ServerName with your server name, ‘Server-IP-Address’ with the IP of your server, and ‘domainname.com’ with your domain.
Here is a detailed video that shows the complete process to login to the cPanel in Hostgator hosting.