I hope this is relevant or at least helps some people out who are trying to run TPM on a new 64-bit operating system.
First, install the game on a 32-bit OS [I installed Win 98 on VMWare Player]. When completed, copy the entire contents of the game directory to 'C:\Program Files (x86)\LucasArts\The Phantom Menace' [Where C is your Windows hard drive]
Copy the entire contents of the reg file below [including 'Windows Registry Editor Version 5.00] into Notepad and save file as Phantom.reg
Windows Registry Editor Version 5.00
[HKEY_LOCAL_MACHINE\SOFTWARE\WOW6432Node\LucasArts Entertainment Company LLC]
[HKEY_LOCAL_MACHINE\SOFTWARE\WOW6432Node\LucasArts Entertainment Company LLC\The Phantom Menace]
[HKEY_LOCAL_MACHINE\SOFTWARE\WOW6432Node\LucasArts Entertainment Company LLC\The Phantom Menace\v1.0]
"Executable"="C:\Program Files (x86)\LucasArts\The Phantom Menace\\WMAIN.EXE"
"Install Path"="C:\Program Files (x86)\LucasArts\The Phantom Menace"
Change 'Z' to whatever letter your CD-ROM drive is.
Merge the file once saved (right click the file to bring up the option). You can now run TPM.exe
Hope this helps