I finally fixed the problem by changing my Web.config file, adding the two lines below that reference the UrlRoutingModule. Do not add the preCondition="managedHandler"
attribute!
<configuration>
<system.webServer>
<modules>
<remove name="UrlRoutingModule-4.0"/>
<add name="UrlRoutingModule-4.0" type="System.Web.Routing.UrlRoutingModule" />
</modules>
</system.webServer>
</configuration>
This helpful post by Thomas Marquardt discusses MVC routing in great detail.
Also, if you're troubleshooting your own MVC routing, be sure to check the answers posted by Ferruccio and stead.