Checking consecutive characters in a string
By using the Distinct method and comparing lengths you can get the number you want in one line.  Here's what such a function could look like:

Function CharsToDelete(Of T)(input As IEnumerable(Of T)) As Integer
    Return input.Count - input.Distinct.Count
End Function


Oops missed the part about consecutive chars.  This should do the trick:

Function CharsToDelete(Of T)(input As IEnumerable(Of T)) As Integer
    Return input.Where(Function(x, y) x.Equals(input(y + 1))).Count
End Function


You don't need to split the text into an array.  The Lines property of the TextBox already does this:

Dim inputArr As String() = txtInput.Lines