Run to the right and ignore the lever for now, continue past the cart with the ladder and jump up the other side. Continue onwards and in the far right side of the area you will find a mine cart. Pull it back to the left and leave it to sit beneath the lever that is visible near the top of the room.
Run back to the cart with the ladder. Push it as far as possible to the left hand side. Climb up the ladder and ride it to the left. Jump out and head to the switch. Wait for the cart to reach the other side of its pit and then turn on the power switch when the cart-ladder is almost at the left hand side of the area. Jump onto the ladder and ride it back to the right. The platform beneath it will rise and allow you to jump from the ladder onto the platform above and to the right.
Once on the platform, move to the right and jump to the switch across the gap. You should fall safely into the mine cart below.
The mine cart will start to move forward. After a short while, you will see a ladder approach in the dark. Jump up to it and get onto the platform above. Let the mine cart get slightly in front of you and follow behind it. A circular saw will start tearing up the platform you are standing on, when safe to do so, run and jump over the saw into the mine cart below.
When the mine cart leaves the electrified floor, jump down to the solid ground below. Do not jump up onto the ledge, as the mine cart will continue into an alcove, hitting a switch here and electrifying said ledge above. When the mine cart comes to rest, pull it out of the alcove and push it up the hill to the left. When you push it, it will continue upwards for a few seconds, before it starts to roll back down the hill towards the switch again. So push it uphill slightly, then jump onto it and from there quickly jump up to the platform above, being sure to run and jump as many times as possible to get to the other side of the electrified floor ASAP.