The Fall of Rome does not install in its own folder, so it overwrote your original RTW game files..... I believe it states that fact in the download thread.
What you need to do is - uninstall RTW/Barbarian Invasion.
- reinstall RTW/Barbarian Invasion
- make a copy of you RTW folder by right clicking on it and selecting copy
- paste the copy next to your original folder. The copy should say
Copy of - Rome Total
- rename the folder FoR
- When installing point the installer toward that folder not your original one
- if done correctly you now will be able to play both RTW and FoR