Fix SQL Server Connection Issues Fast

1. Check network connection: Ensure that there is a stable network connection between the database server and the client, and try using the ping command to test the network connection.
2. Check the status of the database server: make sure it is running and the service is starting up correctly. You can try restarting the database server service.
3. Check the firewall settings: Sometimes the firewall can block communication between the database server and the client, you can try disabling the firewall or configuring firewall rules to allow database connection.
4. Check the username and password: Make sure to use the correct username and password to connect to the database server, as sometimes an incorrect password can also lead to connection failure.
5. Check the database instance name: if a named instance is being used, make sure to specify the correct instance name in the connection string.
6. Check the connection string: make sure that the database server address, port number, database name, and other information in the connection string are filled out correctly.
7. Check database permissions: Ensure that the user accessing the database has sufficient permissions, you can try connecting to the database using the sa account for testing.

If the methods above do not solve the problem, one can try checking the log files on the database server to analyze in more detail the reasons for connection failures. Additionally, using other tools or client software to connect to the database can help determine if the issue lies on the server or client side. If the issue persists, it is recommended to contact the database administrator or technical support for further investigation and resolution.