See comments in code as well as disabled lines and added lines and changes. Minimal changes to your code only:
Sub File_Update2()
Dim WBQ As Workbook
Dim WBZ As Workbook
Dim varData As Variant
Dim varNumber As Long
Dim lngLastQ As Long
Dim RowCountOfCopiedBlock As Long, Destn As Range
'Dim numberrows As Integer
'Dim countrows As Integer
'Dim i As Long
On Error GoTo errExit
Set WBZ = ThisWorkbook
WBZ.Worksheets(1).UsedRange.ClearContents 'changed
Set Destn = WBZ.Worksheets(1).Range("A1") 'added; change to A2 if you want stuff to start on row 2.
varData = Application.GetOpenFilename("File(*.xl*),*.xls", False, "Please mark selected file(s)", False, True)
With Application
.ScreenUpdating = False
.EnableEvents = False
.Calculation = xlCalculationManual
End With
For varNumber = LBound(varData) To UBound(varData)
Set WBQ = Workbooks.Open(Filename:=varData(varNumber))
'ThisWorkbook.Activate
lngLastQ = WBQ.Worksheets(1).Range("A1").End(xlDown).Row
RowCountOfCopiedBlock = lngLastQ - 15 + 1
With WBQ.Worksheets(1) 'changed from WBZ
'sRow = .Cells(Rows.Count, "C").End(xlUp).Row + 1'Destn handles this.
' WBQ.Worksheets(1).Range("A15:Y" & lngLastQ).Copy
'.Range("C" & sRow).PasteSpecial Paste:=xlPasteValues
Destn.Resize(RowCountOfCopiedBlock, 25).Value = .Range("A15:Y" & lngLastQ).Value
Destn.Offset(, 25).Resize(RowCountOfCopiedBlock).Value = .Range("D8")
' eRow = .Cells(Rows.Count, "C").End(xlUp).Row
' .Range("AA" & sRow).AutoFill Destination:=.Range("AA" & sRow & ":AA" & eRow), Type:=xlFillCopy
Set Destn = Destn.Offset(RowCountOfCopiedBlock)
End With
WBQ.Close
Next varNumber
With Application
.ScreenUpdating = True
.EnableEvents = True
.Calculation = xlCalculationAutomatic
.CutCopyMode = False
End With
Range("A1").Select
MsgBox "In total " & UBound(varData) & " files were combined.", 64
Exit Sub
errExit:
With Application
.ScreenUpdating = True
.EnableEvents = True
.Calculation = xlCalculationAutomatic
End With
If Err.Number = 13 Then
MsgBox "No files were selected"
Else
MsgBox "An error occured!" & vbCr & "Error No.: " & Err.Number & vbCr & "Error Description: " & Err.Description
End If
End Sub