This is equal to the URL Rewrite I have created via the URL Rewrite module... No Dice.

I went into DNN per your instructions and same thing. I still get "Page Not Found" when going to aumc.net

Server Variable: Specifies the Server Variable to use when filtering incoming requests. A complete list of valid Server Variables can be found on MSDN.	HTTP_HOST
Operation: Select the operator to use when comparing the incoming request against the specified server variable and value list.	Equal
Match Value: Defines the value of the servervar that triggers the rule. For a regex rule, the value should be a regular expression that used as a matching expression. If this is not a regex operation, then value can be a semicolon delimited list of values.	AUMC.NET
Action: Select the action to perform if the incoming request matches this rule.	PermanentRedirect
Location: Enter the URL to redirect the user if the incoming request matches this rule. This value is only used for Redirect and PermanentRedirect actions	http://www.aumc.net

Maybe there is a problem with your Hosting Configuration.

In your GoDaddy Hosting Control Center look at Settings\Domain Management. 
You should have a doman name of aumc.net pointing to the folder where you have installed DNN.  I did not inlucde the www nor did I add a subdomain of www. 
Next look at Settings\DNS Manager. 
You should have an A (Host) record of @ pointing to an IP Address.  Then you should have a CNAME (Alais) record of WWW pointing to @. 

Good Luck,
Greg

 I've now gotten it to go to the default IIS page instead of the "Page Not Found." The URL Rewrite still doesn't seem to be redirecting it though.

Fixed it! Here is what I did.

1. We have an internal DNS so I added a Host(A) pointing to the new IP.
2. I added the binding of aumc.net to my web site in IIS.

This seemed to solve my problem. Thanks for everyone's help! It was much appreciated!