Add this in your header:
using System.Runtime.InteropServices;
Place the variable declarations on the class level :
[DllImport("User32")]
private static extern int keybd_event(Byte bVk, Byte bScan, long dwFlags, long dwExtraInfo);
private const byte UP = 2;
private const byte CTRL = 17;
private const byte ESC = 27;
Finally on the event where you want to open start menu use :
keybd_event(CTRL, 0, 0, 0);
keybd_event(ESC, 0, 0, 0);
keybd_event(CTRL, 0, UP, 0);
keybd_event(ESC, 0, UP, 0);
The start menu will open.