Sorry, I don't know a sure solution to your problem. This is something I've worried about. I think this design (with this very thin plug) is one of the weakest parts of the power supply.
I used to repair electronics and some of the techs have a very fine set of needlenose pliers. With these, they may be able to get enough of a grip to pull the broken piece out of the plug. You could call a few of the local electronics repair shops and ask if they think they can do this, or if they would be willing to look at it. If they can reach it, it should only take a second to remove it, and should cost next to nothing. Doesn't necessarily have to be a computer tech, just someone who knows what he's doing.
As far as the plug is concerned, you should be able to find a replacement. Take it to an electronics parts distributor and they may be able to help you. It should be a very minor task to have the new plug soldered onto the end of your power supplie's wire lead.
Again, this is a minor task and it shouldn't cost you more than a few bucks, if you find an ethical tech. It would just take a few moments work to get this replaced.
Please let us know how you get it fixed, I'm sure this won't be the last time we hear about this.