First step (if you dont want to redo your video settings and other settings) is to backup the preferences folder of EB: your RTW install folder\EB\preferences. For instance you can place it on your desktop until your done reinstalling.

The best way is to uninstall EB, then uninstall RTW and make sure your RTW folder is gone. In the meantime download the latest full installer of EB. Its better to use that then incremental patches (use the patches if your internet is real slow)

Then start fresh with RTW 1.0, patch it to 1.3 and then to 1.5.
Now (if you have enough space on your HardDrive) copy your entire RTW folder and rename the copy to "RTW 1.5 EB" or something similar and install EB into that folder.

Then you can proceed to install BI and 1.6 and PBEM into the original folder, which contains RTW 1.5.

Oh and you can now move the preferences folder back if you made a backup.