February - last edited February
Originally this post was about how Pinnacle Station and BDTS would prompt with "Mass Effect not found". I worked around that by creating a fake "masseffectlauncher.exe" file in my Mass Effect directory and they installed.
Well, now when I launch Mass Effect, I'm prompted to re-enter my registration key. I DID successfully launch Mass Effect before installing the DLC, so I know that the DLC broke it.
The prompt was pre-populated with a code that it would not accept. I found the Pinnacle Station code from the EA Help article on the topic and tried that, but it wouldn't accept that either.
I don't have a registration code. I bought the game on Steam originally, and somehow it was transferred to Origin. It's been so long that I don't remember that process. I've played Mass Effect many, many times without this ever coming up.
So you are installing the game with Origin?
If so you don't have to install the DLCs separately, (and it will lead to problems as you found out.) they are part of the main download.
Try to repair the game. (in Origin > Game Library > right click ME > Repair)