You've probably got some surgery ahead of you. Open up the offending controller and take out the flex circuit, unfold said flex circuit. At the folds, there's probably a *LOT* of scorching or carbon. Clean this scorch as best you can with a pencil eraser, or some Rubbing alcohol/contact cleaner and Q-tips. If the traces are lost because there was so much heat (i.e. holes), you're probably S.O.L. You may need a donor Inty to get a new flex circuit then.
If the flex plastic is intact, but the traces are gone, you have a risky option: trace repair. Get some of that conductive copper paint used for car back-glass defrosting available at auto repair stores; the types used to re-trace those 'lines'. Re-paint the traces using as little copper paint as possible, to prevent shorting. I use a round toothpick, only putting copper on the tip. Let the paint dry 24 hours, and then re-fold the flex circuit and cross your fingers.
My own attempts have only been 50-60% successful with this, but it better than sitting on my thumbs and doing nothing.