To make it easier for everyone else, I've edited your code above to be more readable.
*** I DID NOT MAKE ANY CHANGES TO YOUR SUBROUTINE IN THIS POST ***
It actually looks like you put the ImportTextLines subroutine in the middle of your DoTheImport subroutine, and the DoTheImport subroutine calls ImportTextFile sub, not ImportTextLines. But either way here is your code, formatted.

[vba]Public Sub DoTheImport()
Dim FName As Variant
Dim Sep As String
FName = Application.GetOpenFilename _
(filefilter:="Text Files(*.txt),*.txt,All Files (*.*),*.*")
If FName = False Then
Msgbox "You didn't select a file"
Exit Sub
End If
Sep = InputBox("Enter a single delimiter character.", _
"Import Text File")
ImportTextFile CStr(FName), Sep
End Sub
Sub ImportTextLines()
Dim RowNdx As Integer
Dim ColNdx As Integer
Dim WholeLine As String
Dim FName As String
Application.ScreenUpdating = False
ColNdx = ActiveCell.Column
RowNdx = ActiveCell.Row
FName = "D:\test.txt"
Open FName For Input Access Read As #1
While Not EOF(1)
Line Input #1, WholeLine
Cells(RowNdx, ColNdx).Value = WholeLine
ColNdx = ColNdx + 1
Wend
Close #1
End Sub[/vba]