If you are familiar with network tools...have you tested connectivity to port 1433? either with a port scanner to validate that the port is open and listening, or with another tool to see if you actually connect on 1433?
Otherwise, if you have SQL Server Management studio installed on that client computer, you can check to see if you can connect and if you can, there may be some other issue related to ODBC. Not sure...since you havent provided any error information.
After I check the ODBC setup when there was a small mistake in the name server and the server alias name that caused the failure of the connection to the existing database on the server, so I have found a connection failure.
in advance thank you for your attention, best wishes