Wow - sorry to hear about that.
Judging from the photo in your signature, you have a facelifted car, which tells me the OBDII port is the only link to the diagnostic system. Older E46s also have the round port in the engine bay for BMW diagnostics.
If you are able to extract the broken pins from the port (I'd suggest patiently attacking the job with the smallest needle nose pliers you can find - and some ibuprofen for your back!), PLEASE consider using a Peake tool for diagnostics. They are made for BMWs only, meaning they ignore the often misleading OBDII codes written by the government for emissions monitoring. In addition to being appropriately designed and programmed for YOUR car, they are extremely high quality tools.
We carry the full line of Peake products at low prices and include free priority shipping for domestic orders.
Have a look at the article in my signature titled "Is your check engine light on?" for more information about the tools.
Best of luck with the pin extraction!
Ken