Hi Bill Westwater,
I understand your pain - the R:TW installer sometimes fails to delete the relevant registry entries, henceforth confusing the CD into thinking that R:TW still is installed.

Don't worry though, you can quite easily remove these keys, although you do require adminstrative permissions to do this:

Firstly click start, and then select run.

Type into the provided box "regedit". After a short pause, the registry editor should open.

Select "HKEY_LOCAL_MACHINE", and then from there select "SOFTWARE", and, from there, open up "The Creative Assembly".

Once you've entered The Creative Assembly's category, delete the section titled "Rome - Total War - Gold Edition".

After that, select the "-" button next to the "HKEY_LOCAL_MACHINE" category.

Once you've done that, open up "HKEY_CURRENT_USER", and, following the same process as before, move on to open up "SOFTWARE" and "The Creative Assembly".

As before, delete the section titled "Rome - Total War - Gold Edition".

After that, close down the registry editor, and attempt the installation again.

Hope this help you, good luck!