The link xQbert gave you shows you the concept, but it might get a little confusing when you have another count already in your select.
You need to remove your group by, and use over on both your counts, limiting one to just count over the group by you already had, and the second to cover the entire range.
You can't use rows unbound preceding in this case since it will create an entry for each row instead of building on the existing result set. But you do need to keep the order by in the over and at the end of the select in sync.
And you also need to add the distinct key word.
SELECT DISTINCT
DATEDIFF(week, 0, IDOC.Import_Date) Week,
DATEADD(week, DATEDIFF(week, 0, IDOC.Import_Date), 0) 'From Date',
DATEADD(week, DATEDIFF(week, 0, IDOC.Import_Date), 0) + 6 'End Date',
COUNT(IDOC.IDOC_ID) OVER (PARTITION BY DATEDIFF(week, 0, IDOC.Import_Date)) 'Total',
COUNT(IDOC.IDOC_ID) OVER (ORDER BY DATEDIFF(week, 0, IDOC.Import_Date)) 'Running Total'
FROM IDOC
INNER JOIN dbo.File_Type FI
on IDOC.File_Type_ID = FI.File_Type_ID
INNER JOIN IDOC_Team_Assignment ITA
ON IDOC.IDOC_ID=ITA.IDOC_ID
WHERE IDOC.Import_Date BETWEEN @from_date AND @to_date
ORDER BY DATEDIFF(week, 0, IDOC.Import_Date)
I can't test this on SQL Server 2008, but I did test it in whatever comes free with VS2013 and I know it works in Oracle. It's worth a shot.
This one was tested on SQL Server 2008 R2 - I hope you aren't in a rush to get this data...
SELECT
DATEDIFF(week, 0, IDOC.Import_Date) Week,
DATEADD(week, DATEDIFF(week, 0, IDOC.Import_Date), 0) 'From Date',
DATEADD(week, DATEDIFF(week, 0, IDOC.Import_Date), 0) + 6 'End Date',
COUNT(IDOC.IDOC_ID) 'Total',
(
SELECT
COUNT(aIDOC.IDOC_ID)
FROM
IDOC aIDOC
INNER JOIN dbo.File_Type aFI
ON aIDOC.File_Type_ID = aFI.File_Type_ID
INNER JOIN IDOC_Team_Assignment aITA
ON aIDOC.IDOC_ID=aITA.IDOC_ID
WHERE
aIDOC.Import_Date BETWEEN @from_date AND @to_date
AND DATEDIFF(week, 0, IDOC.Import_Date) <= DATEDIFF(week, 0, aIDOC.Import_Date)
) 'RunningTotal'
FROM
IDOC
INNER JOIN dbo.File_Type FI
ON IDOC.File_Type_ID = FI.File_Type_ID
INNER JOIN IDOC_Team_Assignment ITA
ON IDOC.IDOC_ID=ITA.IDOC_ID
WHERE
IDOC.Import_Date BETWEEN @from_date AND @to_date
GROUP BY
DATEDIFF(week, 0, IDOC.Import_Date)
ORDER BY
DATEDIFF(week, 0, IDOC.Import_Date)
And now I changed that to a CTE which looks cleaner in my mind.
WITH CTE( WeekNbr, FromDate, EndDate, Total) AS (
SELECT
DATEDIFF(week, 0, IDOC.Import_Date) 'WeekNbr',
DATEADD(week, DATEDIFF(week, 0, IDOC.Import_Date), 0) 'FromDate',
DATEADD(week, DATEDIFF(week, 0, IDOC.Import_Date), 0) + 6 'EndDate',
COUNT(IDOC.IDOC_ID) 'Total'
FROM
IDOC
INNER JOIN dbo.File_Type FI
ON IDOC.File_Type_ID = FI.File_Type_ID
INNER JOIN IDOC_Team_Assignment ITA
ON IDOC.IDOC_ID=ITA.IDOC_ID
WHERE
IDOC.Import_Date BETWEEN @from_date AND @to_date
GROUP BY
DATEDIFF(week, 0, IDOC.Import_Date)
)
SELECT
A.WeekNbr,
A.FromDate,
A.EndDate,
A.Total,
(SELECT SUM(B.Total) FROM CTE B WHERE B.WeekNbr <= A.WeekNbr) 'RunningTotal'
FROM
CTE A
ORDER BY
A.WeekNbr