The home button usually consists of 2 cables ~ one ground and one +.
The ipad reacts to when they touch together (when you press the home button)
Look at the broken cable, and you will probably see these 2 lines. Scratch them up with a sharp razor to expose the copper wire. Once you expose it, you can put some solder, use a little wire, and solder them together.
Shouldn't be too difficult assuming you've done soldering work before.