Check the LoginMode registry key. The path for this key for each version can be found below.
If the value is 1, it's Windows Authentication. If the value is 2, it's Mixed Mode Authentication.
For 2000: HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Microsoft SQL Server\' + @sqlpath + '\MSSQLServer\
For 2005: HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Microsoft SQL Server\MSSQL.1\MSSQLServer\
For 2008: HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Microsoft SQL Server\MSSQL10_50.MSSQLSERVER\MSSQLServer\

