I don't think that you're going to be able to use the Simple CASE with between. Change your query to use the Searched verion

SELECT dbo.corooms.roomname,
	case 
	  when m.begintime between CONVERT(varchar(15),m.begintime, 110)+' 07:00:00' and CONVERT(varchar(15), m.begintime, 110)+' 14:59:00' then 1
	  else 0
	end as ShiftType1
...

-Mike