What are the symptoms? What error messages do you get?
If it has anything to do with required libraries, you can learn which libraries it requires using Matt Pietrek's PEdump utility found here http://www.wheaty.net/downloads.htm
to look through the Imports Table.
For each DLL listed in the Imports Table, make sure that both machines have the same exact DLL installed. Windows had a superior design philosophy, but it was implemented with one major flaw: no version control for DLLs. If your program requires a newer (or older) DLL than the one installed on the foreign host, then problems may occur.
The "windows way" to solve these problems is currently just to copy the appropriate DLLs to the application directory (in addition to the application EXE). So, for example, my SDL application might find itself installed in a directory like
C:\Program Files\MyApp\> dir/a-d/b
myapp.exe
SDL.dll
SDL_image.dll
SDL_mixer.dll
zlib1.dll
C:\Program Files\MyApp\> _
or some such... since the exact SDL library DLLs may vary between applications...
How's that for some grief?