this.comboBox1.BackColor = System.Drawing.Color.White;  //or any other color
this.comboBox1.DropDownStyle = System.Windows.Forms.ComboBoxStyle.DropDownList; //it has to be that style

private void radioButton1_EnabledChanged(object sender, EventArgs e)
{
    if (((ComboBox)sender).Enabled)
    {
        // set BackColor for enabled state
    }
    else
    {
        // set BackColor for disabled state
    }
}

public class ComboBoxCustom : ComboBox {
    [DllImport("gdi32.dll")]
    internal static extern IntPtr CreateSolidBrush(int color);

    [DllImport("gdi32.dll")]
    internal static extern int SetBkColor(IntPtr hdc, int color);

    protected override void WndProc(ref Message m){
        base.WndProc(ref m);
        IntPtr brush;
        switch (m.Msg){

            case (int)312:
                SetBkColor(m.WParam, ColorTranslator.ToWin32(this.BackColor));
                brush = CreateSolidBrush(ColorTranslator.ToWin32(this.BackColor));
                m.Result = brush;
                break;
            default:
                break;
        }
    }
}