Can you not just reattach the wires to each other where they were cut?
When the wires were cut, you ended up with a car side, and a key side. You'll only be using the car side wires at this point. You'll take the heavy gauge white (12v+) wire, and use it on the Starter toggle and the Accessory toggle. Take the other side of the starter toggle and attach the red (starter) wire. Take the other side the accessory toggle and attach the blue/red (accessory) wire. Take the heavy gauge black (12v+) wire and attach it to both Ignition #1 and Ignition #2 toggles. Take the other side of ignition #1 toggle and attach the black/white (ign.#1) wire. Take the other side of ignition #2 toggle and attach the black/yellow (ign.#2) wire.
If you don't have separate toggle switches for each ignition wire, then connect both black/white and the black/yellow together.
After everything is connected, to start the car, you'll need to turn on both ignition toggles, then use the starter toggle until the car starts. The accessory toggle only needs to be switched on after the car is running. However, the accessory toggle isn't actually necessary to make the vehicle run, but controls the radio and other creature comforts. Turn all off when you wish to turn the car off.
Keep in mind there are other wires running up the steering column. Including headlight, parking light, cruise control, horn, among others. This will only start the car and allow it to run. You will also still need the key in the keyhole or else your steering will lock up.
Good luck, and lemme know if you have any other questions.