Defeat all enemies. Go to the left and take a long LEGO piece. Put it on the trails and destroy all boxes nearby. Finish repairing the trails with all LEGO pieces.
On the right side you will notice a machine with dynamite. Use the lever and TNT will fall from the machine. Take it and throw it at the pile of LEGO on the right side. Make a cart from all LEGO pieces and repair it using the wrench (to find it destroy all the boxes in cave). After repairing it, push it all the way to the left.
Go to the left side of the room and stand with Indy on the brown lift. Change the character and use the mechanism nearby. As Indy go strait on the platform and use your whip. Use the lever and the ladder will appear. Jump on the right side and wait for all of the characters to join you. When all characters will stand on the foot-bridge, cart will be lifted. Jump down and climb up using ladder on the right side. Push the cart forward.
Now its time for a cart ride. You need to use your shovel to change all red signs into green. You can lean from the carts to left or to right and change your characters. The cart ride consists of two mini-levels. First one is very easy. You only need to hit all the signs. Second one is little more difficult. You need to change your drive course to hit all of the signs. Carts originally are riding on the right side of the trails but one sign which you need to hit is on the left trail. To enter this trail you need to change you ride course. Notice, that in one place there are signs with arrows. Just before this signs is a mechanism which is changing the direction carts are riding. Hit it with Indy and you will enter left trail and will be able to hit all signs. You can change your riding course as many times as you want. This chapter will end when you will hit all of the signs.