I have a feeling it should have been installed into Program Files(x86), not Program Files.
The standard Program Files folder (not the one with x86 at the end) is meant for 64-bit applications. The one with x86 is for 32-bit applications. Even though it has a similar name, the ProgramData folder is where some programs store their data (not the program itself)
Trainz, from what I am aware, is a 32-bit application and needs to be installed accordingly.
Also, when running Trainz, make sure you run it as administrator, and, as said above, SP1 should be installed as well (if it is installed into Program Files(x86) and the patch is run as an administrator and straight after installing Trainz, it should work correctly - expect a wait of up to 45 minutes while installing the patch.
(I should know, I also run Windows 7 Home Premium 64-bit)
EDIT: A warning for people using XP SP3 compatibility mode, if you are using the Just Trains version or one that requires the disc to be in on launch, it will fail to recognise the disc as being there. Also, Trainz does not seem to like running in compatibility mode - it will run in Windows 7 without compatibility mode)
Shane