If the AC doesn’t turn off, it may be time to clean the condensing unit. Dirty condenser coils won’t give off heat efficiently and will keep the unit running.  Another possibility: The contacts on the outdoor run relay may have welded together—something that can happen over time because of frequent electrical arcing at the relay. Before checking the run relay, turn off the power to the furnace and the condensing unit. Next, disassemble the relay and pry apart the contacts. This should do the trick until you buy a replacement—which you should do soon.
Ground source, or geothermal, heat pumps are similar to ordinary heat pumps, but instead of transferring heat to or from outside air, they rely on the stable, even temperature of the earth to provide heating and air conditioning. Many regions experience seasonal temperature extremes, which would require large-capacity heating and cooling equipment to heat or cool buildings. For example, a conventional heat pump system used to heat a building in Montana's −70 °F (−57 °C) low temperature or cool a building in the highest temperature ever recorded in the US—134 °F (57 °C) in Death Valley, California, in 1913 would require a large amount of energy due to the extreme difference between inside and outside air temperatures. A few feet below the earth's surface, however, the ground remains at a relatively constant temperature. Utilizing this large source of relatively moderate temperature earth, a heating or cooling system's capacity can often be significantly reduced. Although ground temperatures vary according to latitude, at 6 feet (1.8 m) underground, temperatures generally only range from 45 to 75 °F (7 to 24 °C).
The cost to replace a central air conditioner is about $5,000. However, this price varies depending on the size of your home and the difficulty of the project. It can cost as much as $12,500 to replace an AC unit. The labor required to remove and dispose of the old system adds to the price. The size of your home, brand of AC unit and ductwork complexity can all raise the cost as well.
It seems all the average costs for a complete heating and cooling system replacement I've found on websites are usually at least 1/4 less, mostly half lower, then quotes I've gotten from companies. The worst quote I got was from One Hour Heating & Air Conditioning (the company with the Mike Rowe commercials), for over $15,000! I finally settled on a Carrier dealer, for $10,700 & I'll get $950 of that back in energy co rebates eventually. The company I went with's basic system would have been around $8800 (the only one that sorta matched up with web avg cost). They did all the correct planning as far as I could see, not like One Hour, who just showed me a price guide for the same size units already in place. And they do all the rebate paperwork and submit it to the energy co, One Hour never even mentioned possible rebates! Plus Carrier gets above avg reviews. I would have greatly liked a price under 9 grand, but this company got me 0% APR financing, so at least nothing out of pocket. My advice is stay away from national chains, and shop around with local area companies. Of course, One Hour says local companies will fold before you need warranty service lol. For their cost, there should be a technician living in his work van outside my house hahaha.
An air conditioner's compressor contains a refrigerant. As it works, it sends this refrigerant through the system. As warm air blows across the coil that carries this refrigerant, the heat transfers to the refrigerant (cool always absorbs warm). A fan moves the cooled air through the ducting and out of vents that lead into the rooms of your house. The refrigerant returns to the compressor where the absorbed heat is moved outside. The refrigerant is then sent through the coil once again to continue the cycle.

HRV/ERV Ventilators: These whole-house ventilators exchange air. They are ideal for homes with what is called a “tight envelope,” homes where house wrap has been applied and airgaps in the attic, around windows, doors and outlets have been sealed. Air in these homes becomes stale and polluted, so exchanging the air is important to IAQ. Heat recovery ventilators (HRV) are designed for cold climates. Energy recovery ventilators (ERV) are best for warm climates.  Your cost for an installed HRV or ERV will range from about $2,000 to more than $5,000 based on its capacity and features.

In modern buildings, the design, installation, and control systems of these functions are integrated into one or more HVAC systems. For very small buildings, contractors normally estimate the capacity and type of system needed and then design the system, selecting the appropriate refrigerant and various components needed. For larger buildings, building service designers, mechanical engineers, or building services engineers analyze, design, and specify the HVAC systems. Specialty mechanical contractors then fabricate and commission the systems. Building permits and code-compliance inspections of the installations are normally required for all sizes of building.
Before opening the electrical cover on the A/C unit, be sure to shut off all power to the compressor unit and the indoor furnace or air handler, and verify that it is off. Note that this may mean shutting off a circuit breaker that serves the furnace and air handler, and then, near the compressor, pulling out the disconnect block (or shutting off the 220-volt power) to the outdoor compressor.