Base on your description, you can ping the SQL Server and can connect using SSMS from Windows 7 machine, so the SQL Server remote connection is enable.
Generally, we don’t recommend that turn off Windows Firewall. There are three ways to configure the Windows Firewall settings to allow SQL Server Access:
• Windows Firewall item in Control Panel
• Microsoft Management Console (MMC)
For more details, please refer to this
The above is just a suggestion for you. So what type of program are you using? .NET application or something else? Please provide the specific connection string. By default SQL Server Express Edition is installed as named instance “SQLEXPRESS”, so you have
to add the instance name to the server name, like “YourMachineName\SQLEXPRESS” in the connection string, also please ensure that the SQL Server Browse Service is running. You can take a look at this website regarding SQL Server Connection String:
If the above suggestion can’t work for you, please share the SQL error Log for further troubleshooting.