This problem is down to you passing NT / Windows account information in an application that expects you to be using SQL Server authentication.
Is it an in-house application or a third party application? How are you telling it what user ID to use?
For example, SQLCMD has two ways of connecting - either submit a userID & password (switches -U and -P respectively), in which case it uses SQL authentication, or tell it to use Trusted authentication (switch -E) in which case it passes over your windows login credentials.
To generate the equivalent error with SQLCMD, you would run SQLCMD -S -U -P .
If it's an in-house application, check the Connection String, and have a look at http://www.connectionstrings.com for further information.
If it's a third party application, then if it uses an ODBC DSN, then have a look at the settings for that and make sure it works stand-alone (there's a helpful "Test Connection" button). Or have a look for the database connection information in the applications config files / registry settings / whatever. Otherwise check the manual!