Final working code, with huge thanks to Ken McKelvey:

WITH DeleteTests

AS

(

SELECT *

,MAX(CASE WHEN TestStatus = 'D' THEN 1 ELSE 0 END) OVER (PARTITION BY KitId, StdBatteryName) AS IsD

,MAX(CASE WHEN TestStatus = 'N' THEN 1 ELSE 0 END) OVER (PARTITION BY KitId, StdBatteryName) AS IsN

,MAX(CASE WHEN TestStatus = 'X' THEN 1 ELSE 0 END) OVER (PARTITION BY KitId, StdBatteryName) AS IsX

FROM PRE_LOAD P

WHERE EXISTS

(

SELECT 1

FROM PRE_LOAD P1

WHERE P1.KitId = P.KitId AND P1.StdBatteryName = P.StdBatteryName

GROUP BY KitId, StdBatteryName

HAVING COUNT(DISTINCT StdBatteryId) > 1

)

)

DELETE FROM PL

FROM dbo.PRE_LOAD PL JOIN DeleteTests DT

ON PL.KitID = DT.KitID

AND PL.StdTestID = DT.StdTestID

AND PL.StdBatteryName = DT.StdBatteryName

AND PL.TestStatus = DT.TestStatus

AND (DT.TestStatus = 'N' AND (IsD = 1 OR IsX = 1))

OR (DT.TestStatus = 'X' AND DT.IsD = 1 AND DT.IsN = 0);