Melody: Here's my take on cardboard and newspaper: If it's got that plastic shiny coating, or a lot of ink, I leave it out. If it's not coated, and not heavily inked (colored) it goes in. I take a trip to an appliance warehouse several times a year to bring back a truck load of appliance boxes. I load just as many as I can get into the bed of the truck and strap them down with ratchet straps. THAT's a lot of cardboard! It goes in the garden, in the orchard, and most recently in a sheet composting area that I've been working on. I laid the cardboard down there, and tossed a few bags full of leaves on top of it (left the leaves in the bags) to keep the wind from picking it up. A few weeks later, I went back to move the leaf bags. The worms had completely eaten the cardboard under the leaf bags, and the ground was COVERED with worms. IMO, the worms have given all the endorsement about the desirability of cardboard as a compost amendment that I need!
ETA: I do take the time to remove all staples, all tape, especially fiberglass tape from the cardboard before it gets used. Some of those appliance boxes also have strings of fiberglass or other reinforcement laid into the middle of them. Any such boxes are rejected for composting.