Instructions
Look for a damaged switch -- a box with a green button that is throwing sparks -- on the right of the bottom of the mine surface elevator shaft.
Click the green button on the damaged switch to turn off the electricity and stop the switch from creating sparks.
Go to the left side of the elevator shaft and jump up onto the flammable liquid barrel. Jump down to the other side of the barrel. This will position your character between the barrel and the left wall.
Push the barrel right past the elevator shaft, the switch and a pile of rocks until you reach the large rock. Push the barrel against the rock.
Return to the switch and press the green button to turn the electricity on and create sparks. The barrel leaked fluid onto the ground as you pushed it, creating a fuse. The sparks should ignite this fuse and explode the barrel and rock, clearing the first part of the passageway.
Turn off the switch, wait for another barrel to drop to the area left of the elevator and push the barrel to the far right side of the passageway past a small pile of rocks and a miner until you reach the rock wall. Push the barrel against the wall.
Go to the switch and press the green button to ignite the flammable liquid on the ground. The barrel will explode and destroy the wall, creating an opening to the lower areas of the mine.