In case you haven't resolved this yet. It seems to me that the web app setup on the second computer is configured to use the wrong version of .Net.
If you are running a 32 bit version of Windows there is an ASP.Net tab in IIS in the web site properties that you can use to set the site to use .Net 1.1.
If you are using a 64 bit version of Windows it's a little more complicated:
First you have to set IIS to run in 32 bit mode (required to support .Net 1.1 web apps). There's some info on how to do that here: http://support.microsoft.com/kb/894435
Second, you need to use a separate tool to set the version of .Net for the specific site to ASP.Net 1.1. The tool I use is called "ASP.NET Version Switcher" and it's available for free here: http://www.denisbauer.com/NETTools.aspx