To reproduce:
- Add some items to the drop down list.
- Set the ReadOnly to true.
- Start the application and show the drop down.
- Type the first letter of an item and use the arrow keys to select new item.

The issue occur when the drop down is closed, the text in the control is selected and a key is pressed.

Workaround:
void radDropDownList1_SelectedIndexChanging(object sender, Telerik.WinControls.UI.Data.PositionChangingCancelEventArgs e)
{
    e.Cancel = true;
}

void radDropDownList1_KeyDown(object sender, KeyEventArgs e)
{
    if (!radDropDownList1.IsPopupVisible)
    {
        e.Handled = true;
        e.SuppressKeyPress = true;
    }
    
}