Paths in various files needed to be changed.
In Web.config:
<defaultDocument>
<files>
<clear/>
<add value="default.htm"/>
</files>
</defaultDocument>
Needs to be:
<defaultDocument>
<files>
<clear/>
<add value="DesktopClient/default.htm"/>
</files>
</defaultDocument>
In default.htm:
<script type="text/javascript" src="Silverlight.js"></script>
Needs to be:
<script type="text/javascript" src="/DesktopClient/Silverlight.js"></script>
And:
<param name="source" value="Web/ARIS2.DesktopClient.xap"/>
Needs to be:
<param name="source" value="/DesktopClient/Web/ARIS2.DesktopClient.xap"/>
The front most slashes in the last two are important because of this answer.