I made a small change and now it works.  Sorry I didn't look carefully at all
the data when I originally tested the code.

the following statement reads 52 values from the old worksheet skipping
cells as requested
  Set OldRange = Sheets(ws.Name). _
     Range("H5:H17,H20:H32,H36:H48,H52:H64")

The code takes 52 weeks of data in one worksheet and puts it in an array
SumArray.  Then goes to next worksheet and add the 52 weeks of data to the
SumAray.  The macro keeps doing this for all worksheets.  Then the macro
write the final array back in the new worksheet.

Sub getolddata()

Const OldBook = "c:\temp\Old Workbook.xls"

Workbooks.Open Filename:=OldBook
OldBkName = ActiveWorkbook.Name

Dim SumArray(52)
For MyWeek = 1 To 52
  SumArray(MyWeek) = 0
Next MyWeek

For Each ws In Worksheets

  Set OldRange = Sheets(ws.Name). _
     Range("H5:H17,H20:H32,H36:H48,H52:H64")
 
  MyWeek = 1
  For Each cell In OldRange
        SumArray(MyWeek) = SumArray(MyWeek) + _
           cell.Value
        MyWeek = MyWeek + 1
  Next cell
Next ws

For MyWeek = 1 To 52
  ThisWorkbook.Sheets("Sheet1"). _
     Range("B6").Offset(0, MyWeek - 1) = _
     SumArray(MyWeek)
Next MyWeek

Workbooks(OldBkName).Close
End Sub