How can I make a ReadOnly TextBox ignore the mousedowns so that you cannot scroll the text or set the cursor

You can do this by deriving the TextBox, overriding the WndProc method and ignoring these mousedowns.

[C#]
public class MyTextBox : TextBox
{
	protected override void WndProc(ref System.Windows.Forms.Message m)
	{	// WM_NCLBUTTONDOWN  WM_LBUTTONDOWN 
		if(this.ReadOnly && (m.Msg ==  0xa1 || m.Msg == 0x201))
		{
			return; //ignore it
		}
		base.WndProc(ref m);
	}
}
[VB.NET]
Public Class MyTextBox
	Inherits TextBox
    
	Protected Overrides Sub WndProc(ByRef m As System.Windows.Forms.Message)
		’ WM_NCLBUTTONDOWN  WM_LBUTTONDOWN 
		If Me.ReadOnly AndAlso(m.Msg = &HA1 OrElse m.Msg = &H201) Then 
			Return ’ignore it
		End If
		MyBase.WndProc(m)
	End Sub ’WndProc
End Class ’MyTextBox