This part:
If Not FileSelected <> "False" Then
        MsgBox "You have cancelled"
        Sheet68.Visible = xlSheetVisible
        Sheet2.Visible = xlSheetHidden
        Sheet68.Range("M28").Value = 33   'PDF Not_Created due to Cancelling.
        Sheet68.Select
    Exit Sub
    End If
is never executed.
It shall be located before "proper" part. So:

Sheets(Array("SOW_STAR")).Select
FileSelected = Application.GetSaveAsFilename(InitialFileName:=x, FileFilter:="PDF Files (*.pdf), *.pdf", Title:="Save PDF as")

If FileSelected = "False" Then
        Sheet68.Visible = xlSheetVisible
        Sheet2.Visible = xlSheetHidden
        Sheet68.Range("M28").Value = 33   'PDF Not_Created due to Cancelling.
        Sheet68.Select
        Application.DisplayAlerts = True
        MsgBox "You have cancelled"
    Exit Sub
    End If

On Error GoTo ClosePDF
ActiveWorkbook.ActiveSheet.ExportAsFixedFormat Type:=xlTypePDF, Filename:=Path & FileSelected & ".pdf", OpenAfterPublish:=False
Sheet68.Range("M28").Value = 1   'PDF Created.
On Error GoTo 0
    Sheet68.Visible = xlSheetVisible
    Sheet2.Visible = xlSheetHidden
    Sheet68.Range("M28").Value = 1   'PDF Created.
    Sheet68.Select
    Exit Sub
Sheet68.Visible = xlSheetVisible
Sheet2.Visible = xlSheetHidden
Sheet68.Select
Application.DisplayAlerts = True

'*******************
'Error Handling Section
'*******************
ClosePDF:
    STARCertPDF.Show
Sheet68.Visible = xlSheetVisible
Sheet68.Range("M28").Value = 22   'PDF Not_Created due to an existing PDF with same name opened.
Sheet2.Visible = xlSheetHidden
Sheet68.Select
Application.DisplayAlerts = True
End Sub
PS: note added swithing back on
Application.DisplayAlerts = True
on all exit routes