The problem is that Find is not finding the cell.
You will find (pun intended) that the following is true:
MsgBox ActiveSheet.Cells.Find(What:="Start Date", after:=[a1], LookIn:=xlValues, _
LookAt:=xlPart, SearchOrder:=xlByColumns, SearchDirection:=xlNext, _
MatchCase:=False, SearchFormat:=False) Is Nothing
The first thing you should do is fix your search so that it finds the cell you're looking for.
Edit:
Maybe a change that would better illustrate the problem is this:
Dim found as Range
Dim startDateCol as Integer
Set found = ActiveSheet.Cells.Find(What:="Start Date", after:=[a1], LookIn:=xlValues, _
LookAt:=xlPart, SearchOrder:=xlByColumns, SearchDirection:=xlNext, _
MatchCase:=False, SearchFormat:=False)
If Not found Is Nothing Then startDateCol = found.Column
MsgBox startDateCol 'This will be zero if the "Start Date" cell wasn't found.
Edit to respond to comment:
'This should find the exact text "Start Date" (case sensitive) in the header row.
'A cell containing, for example "The Start Date" will not be matched.
Set found = ActiveSheet.Range("1:1").Find("Start Date", LookIn:=xlValues, _
LookAt:=xlWhole, MatchCase:=True)
