1. Do you have a firewall, have you opened it for our IP numbers?
2. Is SQL running on the default port 1433 and is this opened via the firewall?
2. Are external connections enabled in SQL Server?
3. Is TCP/IP protocol enabled in SQL Server?
4. Do you have multiple instances of SQL running on that box, in which case we have to specify the instance name in the connection?
5. Can you connect externally (eg maybe tether to your phone and try connecting from outside your network in the same way we are)?