First, you shouldnt be trying to hack a PS2 controller. They just dont work. Arcade buttons arent analog but the PS2 buttons are. Its possible to trick the controller using resistors but its still not the same.
As for the wires in the cable, the PS controllers have space for 9 pins, but only use 8 of them, in addition to this, there is also a metal square on the top of the plug that may be hooked up to one of them, this would act as an extra ground. If you want to learn more on this, then go download the files for the UPCB and open up one of the files for the PS controller. In it will be a list of what each pin in the plug is for.
When I made my PS cord for my UPCB I found all 9 of my wires in the cord to be connected to something. I didnt check for the metal square on the top, but I did find that two of the wires were connected to the ground. In my case these were the black and grey wires.
One question is, are you checking the wires correctly? You should be using a multimeter, connecting one end to one of the pins in the end of the controller, and then finding which of the wires at the other end it corresponds to. If you already know this then thats good, but I am just making sure.
If you checked the wires correctly then it is likely that two of the wires are broken in the MAS stick. The problem would then be to find out which pins those wires are supposed to be going to. My only thought on how to do this would be to strip the insulation until you find where the break is and then test to see which pin it corresponds to from there. Although you might not want to do this unless you are absolutly sure you are going to replace the cord since its going to ruin the old one.