if you don't want to group by dept, then the SUM needs to be outside the CASE structure, like this:
DECLARE @FYStartDate AS DATE
SET @FYStartDate = '2012-07-01'
SELECT PPDate, --Dept,
SUM(CASE WHEN Dept in ('8310', '8330', '8380', '8500', '9360', '9550', '9610') THEN [Value]/520 --measured quarterly
WHEN Dept = '7120' THEN [value] --hard coded
ELSE Value/80 --measured bi-weekly
END) AS 'Earned FTE'
FROM #trends
WHERE Dept not in ('6570','6580','6645','7221','9831') --don't include these dept's
AND PPDate >= @FYStartDate
GROUP BY PPDate--, Dept
ORDER BY PPDate--, Dept