mysql ステートメントのサンプルを作成しました。http://sqlfiddle.com/#!8/0752c/6 に従ってください
および必要に応じてコード:
CREATE TABLE `yourtable` (
`Id` tinyint(4) NOT NULL,
`Name` char(16) COLLATE utf8_bin DEFAULT NULL,
`StartDate` DATETIME NOT NULL,
`EndDate` DATETIME NOT NULL,
PRIMARY KEY (`Id`)
);
INSERT INTO `yourtable`(`Id`,`Name`,`StartDate`,`EndDate`)
VALUES
(1, 'S1', '2013-01-03 11:23:59', '2013-01-04 13:26:12'),
(2, 'S2', '2013-01-04 00:00:00', '2013-01-04 23:59:59'),
(3, 'S3', '2013-01-12 23:59:59', '2013-01-12 22:20:25'),
(4, 'S4', '2013-01-15 18:15:15', '2013-01-17 13:20:20'),
(5, 'S5', '2013-01-20 21:23:59', '2013-01-22 19:26:12'),
(6, 'S6', '2013-01-04 11:23:59', '2013-01-20 19:26:12'),
(7, 'S7', '2013-01-04 11:23:59', '2013-01-20 08:26:12');
SELECT
Id, Name, StartDate, EndDate,
CASE WHEN TIME(StartDate) > TIME(EndDate) THEN 'true' ELSE 'false' END AS TF,
CASE WHEN TIME(StartDate) > TIME(EndDate) THEN DATE(DATE_ADD(EndDate, INTERVAL 1 DAY)) ELSE DATE(EndDate) END AS EndDateUp
FROM yourtable
WHERE
DATE('2013-01-04') BETWEEN DATE(StartDate) AND
CASE WHEN TIME(StartDate) > TIME(EndDate)
THEN DATE(DATE_ADD(EndDate, INTERVAL 1 DAY))
ELSE DATE(EndDate) END
;