The problem
I have an ASP.NET 4.0 application that crashes with a stack overflow on one computer, but not another. It runs fine on my development enviro
Two things I would try before analysing any memory dumps.
Install the remote debugging tool on the web server and try debugging that way. You can find this tool on the Visual Studio install DVD.
Install Elmah. Elmah can be added to a running ASP.NET application for logging and debugging. I would probably go with this option first and it's the least painful approach. http://code.google.com/p/elmah/