Furnace Circuit Board -- The furnace circuit board controls a variety of functions. It not only handles the regular operation of the furnace, it also monitors the furnace's various safety circuits. Over time, vibrations from the furnace can weaken solder point and cause them to separate. Dirt and debris can cause short-circuits that damage the board. Failure of the circuit board can cause a variety of effects ranging from the fan not turning on to the complete shutdown of the furnace.
Sounds like your first hvac company was ripping you off. Ask your new company to go to your coil and see if there is a leak. If there isn't the last company was just lining their pockets. If you have had ducts unhooked for a long time I would recommend duct cleaning, trust me I'm not a fan of duct cleaning myself. I have done hvac for 20 yrs. in GA. When I just bought a home built in 1996, we had all the ducts replaced immediately.
Duct cleaning has never been shown to actually prevent health problems. Neither do studies conclusively demonstrate that particle (e.g., dust) levels in homes increase because of dirty air ducts. This is because much of the dirt in air ducts adheres to duct surfaces and does not necessarily enter the living space. It is important to keep in mind that dirty air ducts are only one of many possible sources of particles that are present in homes. Pollutants that enter the home both from outdoors and indoor activities such as cooking, cleaning, smoking, or just moving around can cause greater exposure to contaminants than dirty air ducts. Moreover, there is no evidence that a light amount of household dust or other particulate matter in air ducts poses any risk to your health.