Do you know the mode of failure? Was it adhesive or cohesive? Cohesive failure is where the contact cement sticks to both substrates and separates in the center, leaving an adhesive layer on both substrates. Adhesive failure is where the adhesive releases from one surface, usually the plywood.
If the mode of failure is cohesive, the laminate can be reattached with heat and pressure. You might want to purchase or rent a "J" roller. Pressure is as important as heat for this operation.
If the mode of failure was adhesive, the laminate can't be reattached with heat. It'll have to be completely removed.
If you have to remove all the laminate, get yourself a good heat gun that moves a lot of air. Once you get the edge started, position the heat gun between the substrates and have someone slowly exert upward pressure on the laminate.