Having to buy a new Xbox 360 controller is like running on a treadmill---money and time spent for going nowhere. Spend your money on a new game instead of replacing your controller, and fix your controller yourself. Your controller won't be pretty, but it will work just how it should, allowing you to save your money thereby allowing you to see the true beauty of your self-repaired controller.
Cut off all chewed, bent or rippled areas of wire so that only smooth undamaged wires remain. Make sure that the wires are the same length on each end. If needed, remove good wire to make the lengths match.
Strip away a couple of inches of the insulation with the wire using the wire strippers. Remove most of the shielding that looks like silver foil, but make sure to leave half an inch because it will be needed later.
Place filling metal or solder at the end of each wire. Separate the coloured wires so they do not touch each other.
Solder the wires of the same colour together with the soldering iron kit. Wrap each separate wire in electrical tape while making sure there is no exposed wire or solder and also making sure not to cover the silver shielding. Wrap all of the wires together into a single bundle while still leaving the shielding uncovered.
Wrap the bundle together in tinfoil so that the foil makes solid contact with the silver shielding. According to Llamma.com, "the shielding helps cut down on interference."
Wrap the entire repaired area in a solid stiff bundle with electrical tape. You want this area to be stiff and not flexible to keep everything together because wiggling can cause the wires to separate.