Many public locations such; Hotels, Office buildings, Libraries, etc… block the ports that are needed by cPanel and Webmail. This is why you're unable to get to these services. Below is a quick run list of ports that need to be open for you to access the above mentioned services:

Port 2082 – This is your cPanel Port
Port 2083 – This is your secure cPanel Port
Port 2095 – This is your Webmail Port
Port 2096 – This is your secure Webmail Port

If you're in an office, you may want to ask your network administrator to open these ports so you are able to access these services.