Converting an iteration to Async - asp.net

Question

I am returning a large number of DataTable rows, iterating them and pushing the values of each row to a webservice, which then returns a response code (string). Should any errors occur in the webservice, the whole process is stopped and an error shown:
Protected Sub DoStuff(sender As Object, e As EventArgs) Handles lnk_orderCards.Click
Dim dt as DataTable = GetDataBaseData()
For each dr as DataRow in dt.Rows()
Dim f as String = dr.Item("firstname").ToString()
Dim m as String = dr.Item("middleName").ToString()
Dim s as String = dr.Item("surname").ToString()
Dim err as String = String.Empty
Dim result as String = XYZService.DoIt(f, m, s)
Select Case result
Case "ok"
' OK - allow For Loop Next '
Case "e"
err = "Some error"
Case "e2"
err = "Another error"
End Select
If Not String.IsNullOrWhiteSpace(err) Then
ShowError(err)
Exit Sub
End If
Next
XYZService.Complete()
ltl_status.Text = "Success!"
End Sub
I assumed that the above would be a good candidate for an Async approach, especially if the datatable has 1000 rows, as each webservice request could be sent in parallel. However, from MSDN I can't find enough examples on how best to implement Async.
Can anyone recommend a more thorough approach? I have read on MSDN about Task.WaitAll and Task.Factory.StartNew but the examples aren't straightforward. If Task.WaitAll was utilised like this, how do you stop the flow if one (or more) tasks fail?
It's important that all tasks much return success before XYZService.Complete() is called.
Final code based on Stephen's input
Protected Async Sub DoStuff(sender As Object, e As EventArgs) Handles lnk_orderCards.Click
Dim cts As New CancellationTokenSource
Dim dt As DataTable = GetDataBaseData()
Dim rows As IEnumerable(Of Task(Of String)) = (From dr As DataRow In dt.Rows Select DoServiceCall(cts, dr))
Dim results() As String = Await Task.WhenAll(rows)
Dim errors As List(Of String) = (From s As String In results Where s <> String.Empty).ToList()
If errors.Count > 0 Then
ShowError(String.Join("<br/>", errors))
Exit Sub
Else
Console.WriteLine("Success")
End If
End Sub
Protected Async Function DoServiceCall(t As CancellationTokenSource, dr As DataRow) As Task(Of String)
If t.IsCancellationRequested Then
t.Token.ThrowIfCancellationRequested()
End If
Dim f As String = dr.Item("firstname").ToString()
Dim m As String = dr.Item("middleName").ToString()
Dim s As String = dr.Item("surname").ToString()
Dim returnResult As XYZService.ServiceReturnResult = Await XYZService.DoItAsync(f, s, s)
Select Case returnResult.return
Case "ok"
' OK - allow For Loop Next '
Case Else
t.Cancel(False)
Throw New Exception("Web service error: " & returnResult.return)
End Select
Return returnResult.return
End Function

Answer 1

The simplest solution is to use Task.WhenAll. Specifically, you can project (LINQ's Select) each item into a Task (of T) and then do an Await Task.WhenAll.
However, that simple approach will execute all requests concurrently, and will not stop other requests if one of them failed. That's a bit more complicated; I recommend using a CancellationTokenSource to represent the "emergency stop", with each request receiving the CancellationToken and cancelling the source if it fails.
Do not use Task.Run or its even-worse cousin StartNew. Since your operation is asynchronous by nature (an I/O-bound network request), you want asynchronous concurrency (Task.WhenAll), not parallel concurrency (StartNew).