The motherboard is mostly plastic.
Not plastic, FR4 fiberglass-epoxy mix or equivalent. On some motherboards, even PCIe connectors are made of the stuff since it is stiffer than plastic and does not soften as much with heat. Chip encapsulation is often epoxy too.
The most valuable thing on a PCB is probably the copper for places that have equipment to process that. The simplest process involves grinding the PCB and whatever may still be attached into sand-like bits then use specific gravity to sort it out - heavy stuff goes down, light stuff goes up. Each layer ends up containing a relatively narrow range of materials which can then be sent out for further processing/refining.