It's been a long time since I worked on one of those units, but here are a few quick thoughts.
1) There are at least three boards in that tender -- QSI reverse unit for the loco, RailSounds (actually two boards), and the amplifier board. Does everything else work OK?
2) If I remember right, your damaged board serves as both the sound amplifier as well as the constant-voltage source for the tender lighting. Does all the lighting work properly?
3) It's possible that your board could be repaired, if it's just a bad trace. The burning could have been caused by your loose wire coming in contact with something it shouldn't have, and/or having a derailment where the current found the weakest point. If you're comfortable with it, jumper the bad trace with a wire and see what happens.
4) Lastly, check out this part number at Lionel: 6918010T11. It's the scale Turbine tender frame with the sound system (it's unique for the turbine sound) and what MIGHT be the same amplifier/lighting board found in your Southern Mikado. If you choose to go this route, take some good photos of your entire board and e-mail Lionel with the question.
I hope this helps.
TRW