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Hello, so far it sounds like a thermostat electronics failure, however without the full model number of the thermostat and some information how it is wired I can't be sure that it is not a *communicating model.. in which case the problem could be with printed circuit board mounted on the blower inside the furnace/air handler.
If you can tell me how many wires attach to the thermostat, what color they are, and what terminals the wires connect to, (IF if its A,B,C,D and not R, W, Y, G, and C types of numbers the problem could be in the printed circuit board mounted on the air handler blower.
The problem could also be poor contact between one of the pins on the thermostat that connect to the thermostat sub base screwed to the wall.
Tell me a lot about your technical skills sets and if you have a multi meter or not so that I can coach you most effectively.