Repairing a Floppy Molex power connector

No. You need the right connector pin.

Simplest thing to do is to cut a floppy drive power connector with wires off a dead PSU, cut the damaged floppy power off its cable then splice the two.

If you want the more "fiddly" solution that re-uses the exiting connector:

Look very closely at the four brass metal tube-shaped pieces inside the Molex connector, each soldered to one of the wires. As you describe it, one wire has somehow pulled out or broken off on brass piece. Usually each brass piece is made with one or two little arms that stick out from it like a "barb" on a fishing hook. During initial assembly the brass piece is soldered to the end of the wire, and then pushed into the Molex plastic from the back. As it reaches its final position the little barbs push out and snag onto a recess inside the Molex plastic molding. Hence you cannot pull the brass piece back out again.

BUT you can! What you need to do is use a very small screwdriver to reach into the plastic just beside the brass piece (often reach in from the front side) so you can compress the little barb away from the plastic. While holding it that way you can pull the brass piece and its wire out the back again. (In your case with no wire attached, you will need instead to push the piece from the front.) Once you have the brass piece out you can re-bend the barb if necessary to its original position, re-solder it onto the end of the wire, and then re-insert it back into the plastic connector body.

OR you could get a dead psu and splice as needed..
Paperdoc is right it is a "fiddly" thing to do and very easy to damage the connector they are extremely fragile as in not user friendly..It is hard enough to do the Berg connectors for a hdd.... 

The pin in the connector actually was able to be pushed out. I messed with it and I think I'll just cut a dead psu's cable to replace this one and splice them together.