Classic ASP Session State on IIS6 move - losing session variables

We have a critical app that has been running on NT4 under IIS4 and using MTS. The web site takes uploads from users, writes the file to a process directory,which is not the same path as the web app, and there is data stored in a SQL 7 database. There are other programs that are used on the same server that take the data and use to to do some processing and then update the database with the results. There are about 9 seperate classes that are used in the website that were developed in VB6 and the webpage uses   createobject to get a reference and the variables used are session("name) -which is Classic ASP standard practice.
The files that are uploaded by the user are given a new name on the server based on a user identifier and a sequence number. Those names are both displayed after uploading.
The dataload increased dramatically and was causing huge delays in processing. That kicked off the effort to move this to a Windows 2003 box with multiple processors and 8Gig of ram with IIS6 and running SQL 2000.
In testing, the system started reporting errors with the files. It had the original file name, the server filename, and the file it had the error with - was completely different. That filename was from another persons session. The User identifer and sequence number that should have been in the session variables were apparently confused within a very short period of time - all 5 people testing the app saw the same type of error.
We are losing session variables, we have one app pool with one worker process.
There is not a web farm - this is all on one box -- as they do not want to re-architect or rewrite the app.
The box being moved to has SP1 Windows 2003.- SQL 2000 SP4 - IIS6 and nothing else running on the box except this app.  
I am feeling a bit stumped and am reaching out here for some help on what to look for.