You have to have both BHD and TS installed in order for it to work properly.
I've found that the 10th Anniversary collection doesn't play well with the original BHD, so you may want to try uninstalling both BHD and TS, and then re-install them using only the 10th Anniversary collection.
Once that is done, check to see that all the keys on the collection are registered to you. You can do this by going to the forum's navigation bar -> My Account -> Settings -> My Product Keys.
Finally, once you have all of your keys registered to your account, try updating BHD:TS from the game's main menu.
If your update doesn't download correctly, or is otherwise interrupted due to connection problems, you can look for an update .exe that you can download from NovaLogic's business website (www.novalogic.com). Be aware that sometimes has problems, too, but you can be assured that it is the same update you would be downloading if you where using the usual method.
Lastly, if that doesn't work, well... try again. BHD has a history of finicky downloads, and sometimes it magically fixes itself.