HI HomerJ,
I would suggest that you validate that the domain, username, password, db name, and port used (if different from the default 1433) are correct for your installation and the account is administrator permission, UAC is turned off and firewalls and anti-virus are disabled. If your login credentials are indeed correct, I would then look to make sure that the DB installation was completed and defined correctly. You need to insure that the settings on the OS are correct to allow the DB to communicate with the QC/ALM App server.

While logged in as an administrator on your DB server, check the settings for your DB connections by using the Microsoft SQL Server Configuration Manager (to find do the following: Start Menu>All Programs>Microsoft SQL Server> Configuration Tools)

Once Configuration Manager is open, on the left side tree panel, click SQL Server Services.
To the right should be the results pane. Verify that Running appears next to the name of each service under the State column.
If Stopped appears next to any, right-click the name of the service to Start the service.
Next, back to the left panel, expand the SQL Server Network Configuration.
Click on the Protocols for MSSQLServer (if you truly defaulted during install, this will be the name). It could be different if you changed it during installation.
Once on Protocols for MSSQLServer, to the right you should see Protocol Names and Status. Verify that Enabled is present for TCP/IP.
Enable it if disabled by right clicking on TCP/IP name.
Back to left panel and click on SQL Native Client Configuration and expand it.
Select Client Protocols and validate that TCP/IP is Enabled.
Enable it if disabled by right clicking on TCP/IP name.
Last step is to then go back to the SQL Server Services in the left panel and in the resulitng right panel, find your SQL Server (MSSQLServer) or the exact name if you renamed it, and right click on it and click on Restart. This provided that you did find that some of the TCP/IP settings were disabled.

If the above doesn't directly affect/ resolve the issue, thenI would recommend that the following be attempted. Telnet will need to be installed on the system for these to work (it can be installed from the Control Panel> Programs>Add Windows features (these terms may vary depending upon your version of Windows):

First: Open a command window and run telnet -an on the DB server and verify that the server is listening on port 1433 (this is the standard default port, if you have changed your port designation then make sure that you are checking that port as listening. IF they are not then you need to make sure that they are enabled as above and other issues are not blocking them (you will probably need to involve your IT if it is not listening).

Next on the QC/ALM app server: open a command windows and run telnet If the connection is accepted then the QC app server can talk to the DB server, if the connection is denied then the port is blocked on either the DB server or the QC/ALM app server. I would check the firewalls on both and disable them for testing this out. Disable one at a time to see which is causing the issue. Then if the connection is accepted, you can now retry the configuration for the installation.

The installation should now complete without issue and QC should be able to run. You will now need to get with your IT department to figure out whether they want to allow the server to run without the firewall and anti-virus, or if/ how they want to configure the exceptions to allow the communications across the needed ports (group policy exception, firewall exception, etc, it is their decision but the 1433 port must remain open for the DB traffic.

I hope this helps,
Dan