Oh, this brings back unhappy memories of having to repair car decks. Here is my input:
1. The trace is probably burned because the output IC is blown. Very common. If you follow what is left of the trace, to the South in the picture, you will see a Single Inline Package IC, possibly mounted to a heat sink. Look at the part number on the IC and Google it. Select "Shopping." See if any are available. If not, give up, because you will never get this working. If you see some available, next look for a data sheet and print it out. Identify the power pin and output pin. Measure the resistance between the power pin and ground, the power pin and the output pin and the output pin and ground. If you get a low resistance reading on anything, the IC is blown. You will need to replace it and repair or jumper the blown trace.
2. The knobs are glued on with a rubber cement or contact cement. You can try heating them up a bit to aid in removing them.
3. Look at where the mechanism is and where it attaches, and remove whatever is in the way. You may have to remove the main board. If the unit has an LCD display, there will be a flat flex ribbon connected to it. Be very careful not to tear it, or game over.
4. Often you can remove the plastic front (called the nose) and it will allow you to get to the innards.
Good luck!