If the record's StartDate is not today need the WHERE clause "EndDate IS NOT NULL" (all of today's records are included, even ifthey do not have an end stamp).
The test query should return C, D, E and F.
CREATE TABLE #Test (MyId char(1), StartDate datetime, EndDate datetime)
--no end date
INSERT INTO #Test (MyId, StartDate)
SELECT 'A', '2013-10-30 10:00' UNION ALL
SELECT 'B', '2013-11-30 10:00' UNION ALL
SELECT 'C', '2013-12-30 10:00'
--end date
INSERT INTO #Test (MyId, StartDate, EndDate)
SELECT 'D', '2013-10-30 10:00', '2013-10-30 11:00' UNION ALL
SELECT 'E', '2013-11-30 10:00', '2013-11-30 11:00' UNION ALL
SELECT 'F', '2013-12-30 10:00', '2013-12-30 11:00'
SELECT * FROM #Test
CASE WHEN StartDate < CAST(GETDATE() as Date) THEN WHERE EndDate IS NOT NULL END