Are the binaries still there? Do they prevent access to IE, or just decree that it shall not be used as a general browser? What about a thin VB wrapper around the IE html control? No browser controls, just a rectangle to run the app in.
If they run the first version of Windows 95 before IE was bundled with it, chances are they don't have IE. Or maybe they have IE 3.0, and it does not work with the code designed to work with IE 4.0 and higher? NT 4.0 also had an earlier version of IE on it.
Ah fudge, just re-write the ASP stuff in Java, it should then run on any browser that supports Java. Right?