Whoa, I'm not sure that any of those wires/traces are obviously a ground.Following route "B"... There is a piece of copper-strand sticking out of the circuit board (not the white coated wire). That piece used to be connected somewhere to the circuit board. Find out where that "somewhere" is, by tracing it. and then solder a wire between "somewhere" and the ground.
I"d try that before spending any money.
It's obviously a ground, but whatever is on the other "somewhere" end is probably not grounded and probably should be.
The large copper area (light green) is, in all likelihood, the ground plane and neither of those lamp contacts look to be connected to that plane.
Path A will reconnect the two ends of the burnt up trace. Start there (and remove that stubby white wire thing) and see if you that fixes anything.
And remove the other white wire, god knows what that's for.