Advanced Filter "<=Date" does not work?

I just can not get this code to work.

I want it to look for data equal to a user inputted Account Number and Start and End Date. The input bit seems to work, the rest doesn't.

Public Sub Demo()
Dim ResultRowCount As Long

' config here
Const AccountColumn As Integer = 1
Const DateColumn As Integer = 2
Const DirectoryToSaveIn As String = "C:\Test\"


tryAgain:
StartDate = Application.InputBox("Start Date i.e. 01/01/2011", "StartDate ")
If StartDate = False Then Exit Sub

'Validation of date format
If Not StartDate Like "##/##/####" Then
msg = "Entry must be dd/mm/yyyy format"
pt = MsgBox(msg, vbExclamation, "Invalid entry")
GoTo tryAgain
End If
If Not IsDate(StartDate) Then
msg = "Entry must be dd/mm/yyyy format"
pt = MsgBox(msg, vbExclamation, "Invalid entry")
GoTo tryAgain
End If


tryAgain1:
EndDate = Application.InputBox("End Date i.e. 31/01/2011", "End Date")
If EndDate = False Then Exit Sub
'Validation of date format
If Not EndDate Like "##/##/####" Then
msg = "Entry must be dd/mm/yyyy format"
pt = MsgBox(msg, vbExclamation, "Invalid entry")
GoTo tryAgain1
End If
If Not IsDate(EndDate) Then
msg = "Entry must be dd/mm/yyyy format"
pt = MsgBox(msg, vbExclamation, "Invalid entry")
GoTo tryAgain1
End If


AccountNumber = Application.InputBox("Account Number", "Account Number")
If AccountNumber = False Then Exit Sub


' Copy sheet
ActiveSheet.Copy

' Set up Criteria for advanced filter
Range("X1").Value = Cells(1, Account).Value
Range("Y1").Value = Cells(1, Date).Value
Range("Z1").Value = Cells(1, Date).Value
Range("X2").Value = AccountNumber
Range("Y2").Value = ">=" & StartDate
Range("Z2").Value = "<=" & EndDate

' Apply Advanced Filter
Columns("A:W").AdvancedFilter Action:=xlFilterCopy, CriteriaRange:=Range( _
"X1:Z2"), CopyToRange:=Range("AA1:AI1"), Unique:=False


' Get Rid of old data
Columns("A:Z").Delete

ResultRowCount = Cells.Find("*", SearchDirection:=xlPrevious, SearchOrder:=xlByRows).Row

' Save File New Name
Filename = AccountNumber & "_" & Format(StartDate, "mmm_yy") & ".xls"
ActiveWorkbook.SaveAs Filename:=DirectoryToSaveIn & Filename
ActiveWorkbook.Close

'Inform user of results
ln1 = "Location : " & DirectoryToSaveIn & vbNewLine
ln2 = "FileName : " & Filename & vbNewLine
ln3 = "Row Count: " & ResultRowCount & vbNewLine
msg = ln1 & ln2 & ln3
pt = MsgBox(msg, vbInformation, "Process Complete")