Ok that makes sense, but what about on the new one theres a -12v but I dont see one on the old supply? 
Leave it alone like the green wire in my diagram -- same for the -5v wire on pin 9.
It won't hurt the power supply if an output voltage isn't connected.
If the old 3 pin connector was originally connected to anything, connect the line (black), ground (green), and neutral (white) wires from the new to the old 3 pin.
Connect one +5v wire from the new PSU to each red wire on the old 9 pin.
Connect one +12v wire from the new PSU to each blue wire on the old 9 pin.
Connect one ground wire from the new PSU to each black wire on the old 9 pin.
*** Just remember that the black wire on the 3 pin is 120 VAC line power, but the black wire on the 9 pin is ground (DC) -- standard AC wiring colors vs. standard DC wiring colors. ***
BTW, the connector on the new PSU looks like the same style used in the Star Wars Yoke controller, but different gender -- I think the pin numbering will be like this with pin 1 starting on the double flat end, but double check to be sure.

In the pic you posted showing the connector, the upper right should be pin 1, lower right should be pin 3.
Scott