Another thing that seems amiss; there should be THREE areas that you need to input information:
1. "User Name" or "Name"
2. Organization
3. Serial Number
You MUST put a name in the "name/user name" space, or the installer will not run correctly. Secondly, be sure you are typing the serial number exactly as it appears, caps/lower case, dashes/hypens, underscores, etc.
"Organization" can/should be left blank. It does not affect installer.
Your other issue is likely due to needing "administrator authority", and WHERE you are trying to install Trainz.
Before installing, navigate to your disk drive,
Right-click the installer exe file, Left-click "Properties",
Left-click the "Compatability" tab, and at the bottom, check the box for "Run as Administrator",
Left-click the "Security" tab (if available), then left-click the "edit" button.
Left-click each name in the list, in turn, and check the box for "full control" under the "Allow" column.
Save, OK, Save, OK.
Next, Right-click the exe file again, left-click "run as administrator"...proceed as normal, except;
DO NOT install in to either the "Program Files" or "Program Files (x86)" folders. When installing, change the path to either directly on your C:\ drive, or on to another drive, if you have one.