Have you tried this code from Lynn?  This should work.  Another option is to use ROW_NUMBER(), something like this:


WITH UniqueCI AS
  (
   SELECT
    ROW_NUMBER() OVER (PARTITION BY
            ITCI.[Computer Name],
            ITCI.[Service Tag]
           ORDER BY
            ITCI.[Computer Name]
          ) AS RowNo,
    ITCI.[Computer Name],
    ITCI.[Service Tag]
   FROM
    dbo.ImpTbl_ComputerInventory AS ITCI
  )
INSERT INTO dbo.Tbl_ComputerInventory (ComputerName, SerialNumber)
    SELECT
      *
    FROM
      UniqueCI AS UCI
    WHERE
      UCI.RowNo = 1 AND
      NOT EXISTS
    (
      SELECT
       1
      FROM
       dbo.Tbl_ComputerInventory AS ITCI
      WHERE
       UCI.[Computer Name] = ITCI.ComputerName AND
       UCI.[Service Tag] = ITCI.SerialNumber
    );