I've got the same problem. For me the solution arrived when I've runned the program in the compatibility mode (go to mass effect .exe file, right click, and set it to compatibility with 'windows xp serv pack 3'.
With that i was able to run the game. But now i can't load my saves...
Best of luck, anyways...
I tried and I"m still getting the same directX9 message. Should I try re-installing it?
OK I GOT IT TO WORK!
After sitting down and talking to an EA chat person, and going through a bunch of different troubleshooting with Origin and DirectX....the solution was VERY * SIMPLE! Just go into your Origins in game settings and disable the "origin in game" overlay. Worked like a * charm.
