I obtained the connectors from Digi-Key - they are a very useful distributor of electronic components with a good part search engine, no minimum charges, and great shipping options. For a small order like this the USPS first class option is cheap and fast (usually two days for me).
The plastic shell is Digi-key #WM2117-ND, the crimp terminals are #WM9846-ND. I don't know your experience level so pardon me if the rest of this paragraph should go without saying. You'll need a crimping tool to form a reliable electrical connection to the wire, fortunately I was able to borrow one from work. I highly recommend buying extra terminals, I ruined one learning how to use the crimp tool. ;-) At a pinch one might be able to fold the terminal onto the wire with needle-nose and then solder, but you'd have to be very careful to minimize the bulk of the result so that the terminal will still slide into the shell and lock in place.
Note that the rear-most prongs of the terminal crimp around the insulation, where the forward two crimp to the copper strands. The stripped length must be very short and precise to avoid having strands get into the contact area.
Working one wire at a time I clipped it from the burned up shell, stripped it, crimped on the new terminal, and then slide it into the new shell. That way I was sure to put each wire in the correct position of the new shell.
Best of luck!
Edited by Shal, 26 January 2014 - 06:00 PM.