It seems as if the thermostat wire, usually the green one, is somehow touching another wire, likely red, and is keeping the fan running full time. Or your stat is set to "fan" instead of "auto". These are my initial guesses from afar. You could test the wire theory by removing the green stat wire from the control board at the furnace and then let the furnace run another cycle and see if it shuts off. That would at least tell you if the problem is on the wire/thermostat side or the furnace side. If it shuts off, it's on the stat/wire side. If not, the problem is in the furnace.