I simply copied the whole Trainz install folder - the whole kit and caboodle - to an external drive then copied the install back to my new computer's hard drive.
Once everything was copied, I had to reassociate, within Windows Explorer or File explorer in Windows 8, CDP files with Contact Manager and tell my browsers what to do with CDPs.
After everything was setup, I right-clicked on the Trainz.exe, created a shortcut - did a send to Desktop function - and edited the properties to run as Admin.
I've used this process a few times now without any issues with Trainz. It's also a great way to transfer the install to a gaming laptop when traveling.
John