OK, here you go:

Look at the plug you cut off your fan. Orient the connector in the same way this one is, with the little ridges pointed towards you. The wire on the left is negative, the middle wire is positive, the wire on the right is the tachometer/sense wire and should have no connection in your setup, just ignore it completely. Now you know what color is what. Hook up the wire that is the same color as the wire on the left in the plug to negative and the wire that is the same color as the wire in the middle of that plug to positive. Your fan should now function correctly.

Look at the plug you cut off your fan. Orient the connector in the same way this one is, with the little ridges pointed towards you. The wire on the left is negative, the middle wire is positive, the wire on the right is the tachometer/sense wire and should have no connection in your setup, just ignore it completely. Now you know what color is what. Hook up the wire that is the same color as the wire on the left in the plug to negative and the wire that is the same color as the wire in the middle of that plug to positive. Your fan should now function correctly.