ok, i am going to try to clear this up...
the wires on the power supply that plug into the motherboard...
im not sure what you meant by two different ones...
as far as power wires, some of them have a single plug with approxamately 18 wires, and some have a set of two plugs with 6 or so each...
on top of that, some have a small wire set of wires that come out of the supply, and plugs into the board, and this one has two or three wires. this on plugs into the board to control the power supply fan.
on top of those, they all have the wires that power the hard disks, floppies, and cd-roms.
older ones also have a set of 4 wires that go to a physical switch on the front of the tower, whereas newer ones have a small set of wires from the motherboard that go to a set of soft off switch and reset switch.
what type is your supply, and what type is your cousins' supply?
if your supply actually made his turn on, and actually showed the bios boot screen where it tests ram and stuff, but did not do the same thing on yours, then i would maybe assume that it might be a working supply.
booting all the way into windows is a better test though.
you mentioned some white stuff on the power supply board, but im not sure this came from the caps. usually a swollen leaky cap will be covered with a brown resinous substance, almost like terriaki sauce. i did say usually.
sometimes oxidization can form on a circut board, if the unit has been exposed to moisture.
you mentioned having a way to take a picture...
perhaps you could set your power supply, and your cousins power supply next to each other and take a picture of the difference in the cables you mentioned.
it might also help to see a pic of the plugs on his and the sockets on your board that his plugs wont fit into.
again, this is why i hate stuff that is made proprietary, like dell, and gateway, and sony, and hp.
i like things that are swappable.
now as far as a fried cpu keeping the machine from booting, i have seen some fried cpu's simply not go past the boot test, and i have seen some not even start at all. (meaning the monitor never showed anything at all)
i have also seen ram sticks do both of these, and pci cards, and agp cards, so you shouldnt ever simply say that it cant happen.