Excel VBA Sum Data within user input date range - vba

Question

I'm trying to code a macro that will sum data based off a user-input date range. I've got the code worked out to get the user input range and verify that it is a date, as well as convert it to match the syntax of the headers in my data file, but I'm having trouble figuring out how to sum only the months within that date range, with the date range subject to change every time the macro is run.
Here is a screenshot of the workbook. If the user inputs 1/1/16 and 3/31/16, I need the "Sum of Qty" to be a sum of the qty for January, February and March 2016. The same needs to occur for "Sum of Cost." There are multiple tables on the same sheet where this needs to happen and more tables, months, and columns will continue to be added.
Here is a link to the file, if you'd like to see formatting: https://www.dropbox.com/s/bc5okk684livm3a/TestFile_DateSum.xlsx?dl=0
And here is my existing code:
Sub DateRange()
Dim dateString As String, TheDate As Date
Dim dateString2 As String, TheDate2 As Date
Dim valid As Boolean: valid = True
Dim valid2 As Boolean: valid2 = True
Do
dateString = Application.InputBox("Enter Start Date in xx/xx/xx format: ")
If IsDate(dateString) Then
TheDate = DateValue(dateString)
valid = True
Else
MsgBox "Invalid date"
valid = False
End If
Loop Until valid = True
Do
dateString2 = Application.InputBox("Enter End Date in xx/xx/xx format: ")
If IsDate(dateString2) Then
TheDate2 = DateValue(dateString2)
valid2 = True
Else
MsgBox "Invalid date"
valid2 = False
End If
Loop Until valid2 = True
Application.Calculation = xlManual
[C3] = TheDate
[C4] = TheDate2
StartMonth = Month(TheDate) & "/1/" & Year(TheDate)
EndMonth = Month(TheDate2) & "/1/" & Year(TheDate2)
'Application.Calculate
'Application.Calculation = xlAutomatic
End Sub
Any help would be greatly appreciated!