Welcome to the forums. Have you tried to shift into reverse manually by using the manual shifter that came with the ATV? If you can't shift into reverse manually, you may need to adjust your reverse lockout cable. The cable might not be pulling the reverse lever up all the way when you push the red button and pull in the brake lever.
Most 4-wheeler problems are caused by a loose nut connecting the handlebars and the seat!!
You only need two tools in life -- WD-40 and duct tape. If it doesn't move and should, use the WD-40. If it shouldn't move and does, use the duct tape.