Thin'd app won't run - DLL error although DLL file is in package

I am attempting to thinapp an application that does not run natively on Windows 7.

I have a clean XP SP3 machine that I am installing and capturing on. Install and capture goes just fine, Once the package is built. I can run the program locally on the XP machine and I can run the built package on the XP machine. When I store the package on a server and then attempt to access it from a Windows 7 32-bit machine I get an error that it can't locate some DLL files. However, I have confirmed that the files are installed on the XP machine where they are supposed to be and are also in the smae folders in the folder that the package is built from.

Any thoughts?