This is what I'd do to solve this problem:
Private Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) 'Handles Button1.Click
'Parse the two numbers
Dim minValue = Integer.Parse(TextBox1.Text)
Dim maxValue = Integer.Parse(TextBox2.Text)
'Create a list of all possible valid numbers
Dim values = Enumerable.Range(minValue, maxValue - minValue).ToArray()
'Keep only the even numbers if selected
If CheckBox1.Checked Then
values = values.Where(Function (v) v Mod 2 = 0).ToArray()
End If
'Keep only the odd numbers if selected
If CheckBox2.Checked Then
values = values.Where(Function (v) v Mod 2 = 1).ToArray()
End If
'Check there are numbers
If values.Length = 0 Then
TextBox3.Text = "There no available numbers to choose."
Else
'`rnd` here is `System.Random` as I didn't know what `Rnd()` was.
TextBox3.Text = values(rnd.Next(0, values.Length)).ToString()
End If
End Sub