To get the filepath to the Internet Explorer Application you need to access a Registry Key:
using Microsoft.Win32;
using System.Diagnostics;
private string IEKey = @"HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\App Paths\IEXPLORE.EXE";
private void LaunchIE()
{
string IEPath = Registry.GetValue(IEKey,"Path","").ToString().TrimEnd(';') + @"\iexplore.exe";
Process.Start(IEPath);
}