I have a all my user permissions to have full access. Still not working, unless I'm not understanding where you elevate these permissions. I don't know everything about IIS.
Also I'm working with DNN 6.1.3 with IIS7.5 if that makes any difference.

Is it a server at your company, your own or shared hosting? A shared hosting won't let you run an .exe. If it's your company, you might still have some convincing to do to the server admin to let a non interactive user run .exe's.
If it's yours, I guess you can do whatever you want.

Once you have an elevated user set up in Windows, change the identity of the application pool under which the DNN site is running to that user. I am not sure if that's even enough. Make sure only that site is using that pool. You don't want other site to have extra privileges.

If the .exe is from a third party vendor and they don't provide a library, you might be stuck with using the .exe. Otheriwse create a library to do the same functionality and use it in a custom module.

Still not having any luck. Do I need to set anything up in the sites Authentication settings?
Also, currently for testing purposes I'm doing this on my local machine and I'm trying to run cmd.exe and pass in a paramter to basically create an empty
text file. I'm wondering if it's because I'm trying to run cmd.exe that I keep have issues.