Lay your 35-inch plywood flat and horizontal. Lay your 35-inch board flat on top of the plywood, and along the 35-inch edge of the plywood. Screw the board to the plywood at this location. The 35-inch edge of the board should be flush with the edge of the plywood. Repeat this process with the other 35-inch piece of plywood and the other 35-inch board.
Screw your 17-inch board along the 18-inch edge of the plywood. The 17-inch board should be perpendicular to the 35-inch board, and flush with 18-inch edge. Repeat this process on the other 18-inch end of the plywood, and repeat this whole step with the last two 17-inch boards, and other piece of plywood.
Position the two 35-inch pieces of plywood upright and parallel so they are standing on their 35-inch edge and 35-inch board. The distance between the outside edges of the plywood sheets should be 24 inches. Screw your 24-inch sheets of plywood to the 17-inch boards on the 35-inch sheet of plywood; one on each end. You should have a rectangular frame with the outside measurements of 24 inches by 36 inches.
Turn your frame upside down and lay one of you your 36-inch sheets of plywood over the frame. Screw through the 36-inch plywood into the 35-inch board, making sure all the edges are flush. This is the bottom of your treated storage bench.
Turn your frame over so it is upright. Screw your hinges to the inside of the frame. There should be one hinge 6 inches from the left outside corner, and another hinge 6 inches from the right outside corner. Screw the other sides of the hinges to the 36-inch plywood so that when closed, all the corners are flush.