By deleting the game files you may have messed up the registry settings which are still there if you just delete registered/installed stuff.
Try uninstalling the games using the System Control Panel-->Software. If this doesn't work, delete the directories, like you just did. I don't know where the game stores your license information from the download, so make sure you backup this information before you do something that makes a reinstalltion impossible. For example deleting a license and so EA doesn't know any longer that you own the game and wont let you download it again. I must remember you again that I don't know how this download portal handles such things though.
Then get yourself a registry cleaner, like
CCleaner or
RegCleaner. Be careful though these programs are sometimes a bit to heavy on deleting stuff, only select entries to remove where you are 100% sure what they are for. In case of B&W2, well all stuff with Lionhaed and B&W2.
You can also delete the registry entries manually the following way:
1. Go to Start->Run and type in "regedit" to start the registry editor.
2. Browse the registry to:
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Uninstall
3. Mark the Uninstall arm entry and use the search from the menu (or press CTRL+F).
4. Search for "Black & White" (without quotation). This should return two entries with cryptic numbers (e.g. {10631C28-62E5-477C-9B40-40C5EA8219BE}), one for B&W2 and one for BOTG. Delete them both (the entries with the cryptic numbers).
5. Now you should be able to reinstall the game, so do it.
If you are unsure, better ask before you delete something else important!
Also remember that the game offers an repair option to restore it. You can reach it over the System Control Panel-->Software too. Just use the uninstall option and it should give you the repair option too.
Everyone should boycott Ubisoft and their new Online DRM for PC games. This has gone too far in the reduction of the rights of users and I am sick of it! It is not made to fight piracy, but to control the customer.