I am using sql server 2005. TCP/IP is enabled. windows authentication is being used. while trying to connect the server with the Database Engine as server type, I am getting
This error means that given windows user 'name-pc\account 2' does not have access to given instance. You can login with 'sa'(if it is enabled otherwise login with other sysadmin account) and check if 'name-pc\account 2' is exists and enabled.
You can also read more about this error and gain more information HERE
Please read the comments too, some important tips and points reached in comments
You may be missing this setting. SQL Server authentication mode is not enabled on my machine by default. (Remember to re-start the SQL server after this change)