Bill, you might try to pull out the broken key fragment if you have very fine pointed tweezers. If you're very lucky, you might be able to pull it out. Locksmiths probably have better tools to get broken keys out.
You can still lock the car, climb in the passenger's side and lock the driver's side door and then lock the passenger side door, assuming the passenger side lock works flawlessly.
I had to replace the door handle on a '83 SD, and I ordered it from the dealer for about $120 with one key. With the VIN, the keys will match properly. There is something called a "shop key" that has its own key, but then you have a two-key car. Perhaps a locksmith can get the key part out, or make you a new tumbler and put it in for less than a new handle.
I went the new handle route because the door lock tumbler was frozen up. I took the door panel off so I could get the thing put back together easier, but I didn't try it without removing the door panel first.
Robert W. Roe
1984 300SD 173K mi