OK, I'm having the same problem, and I think I've just discovered something new.
Are you all using Mass Effect Trilogy? Because, apparently, both DLC (BDtS and Pinnacle Station) are supposed to be included in Mass Effect Trilogy.
I've just been into regedit, and there are registry entries for all three (the game itself, plus the two DLCs). There are some empty fields though.
But I've installed using Origin and there are no DLCs in the game (the DLC menu is empty).
Also, some of the registry entries don't have values. I don't know enough about the registry to know what should be there. Could someone with a working Mass Effect 1 + both DLCs tell me what should be in my registry? Or where to find the DLC files, if they're installed?
EDIT: And the plot thickens! I think I've found the DLC. They're in the DLC folder in the Program Files\Mass Effect directory. There are two folders named DLC_UNC and DLC_Vegas which, from what I can see on Google, correspond to the two DLCs (Bring Down the Sky and Pinnacle Station). But they don't show up in the game! What's that all about?
FINAL EDIT: OK, I think I've solved it (for people with ME Trilogy, anyway). I uninstalled the game, but left the registry (with the entries for the DLC). I then set Origin to Win XP SP2 Compatibility and run as admin. I then reinstalled ME1 and, voila: both DLCs are there automatically!
I don't know whether you guys are using ME Trilogy but, if you are, you DON'T need to download either of the DLC seperately (even though EA customer support told me I did). They're already there. You just have to get the game to recognise them. Try doing what I did.