In order to execute applications that require elevated privileges, your application must do one of two things:
1: Run with elevated privileges. When you invoke a process, it will see that you are already using elevated privileges and run at the same level.
-or-
2: Create a launcher executable that requires elevated privileges. From the launcher, start the application that needs this privilege level. See this SO answer for more information about process privilege elevation.
HOWEVER
Doing this from a web browser complicates things as all web browsers are sandboxed to prevent malicious code from executing. You will have to put this web site in IE's Trusted Zone to even launch a non-privileged executable.