AC units and thermostats have built-in delay features when they're shut down and then repowered. The delay can be as long as 10 minutes. And, if you've subscribed to an energy-saving device from your local power utility, the unit can take even longer to reset. If you've installed the parts shown and reinstalled the disconnect block, repowered the circuit breaker, turned on the switch at the furnace, moved the thermostat to AC mode and lowered the temperature below the indoor temperature, and the unit doesn't fire up after 30 minutes, it's time to call a pro.
Replacing a capacitor is easy. Just take a photo of the wires before disconnecting anything (you may need a reference later on). Then discharge the stored energy in the old capacitor (Photo 4). Use needle-nose pliers to pluck one wire at a time from the old capacitor and snap it onto the corresponding tab of the new capacitor. The female crimp connectors should snap tightly onto the capacitor tabs. Wiggle each connector to see if it's tight. If it's not, remove the connector and bend the rounded edges of it so it makes a tighter fit on the tab. When you've swapped all the wires, secure the new capacitor (Photo 5).

AC air handler buzzing sounds. Do you hear a buzzing sound when you turn on the thermostat? The only thing that comes on in the house when you turn on the thermostat is the fan relay and fan in the air handler or furnace. Try switching the thermostat HEAT/COOL switch to OFF. Then switch the fan switch from AUTO to ON. The fan (only) should come on. If the air handler makes a buzzing sound, it probably has a bad fan relay or, more likely, blower fan.
Central home air conditioner service systems consist of two major components: a condensing unit that sits outside your house, and the evaporator coil (often referred to as an A-coil) that sits in the plenum of your furnace or air handler. The refrigerant in the A-coil picks up the heat from your home and moves it to the outdoor condensing unit. The condensing unit fan blows outside air through the condensing coil to remove the heat. The condensing unit houses the three parts replaceable by a DIYer: the AC contactor, the start/run capacitor(s) and the condenser fan motor. The condensing unit also houses the compressor, but only a pro can replace that. The A-coil has no parts that can be serviced by a DIYer.
In the middle of summer—even more so in North America—AC repairs are undoubtedly the last thing you want to have to think about. But that won’t keep them from taking place. Fortunately, Service Experts Heating & Air Conditioning is dedicated to completing expert quality AC repair, maintenance and installation throughout the North America area. We certainly don’t want you to be stuck in an uncomfortable home during the hottest days of summer.
My Carrier furnace occasionally (one-two times a day) does not start. It shows error code 15 ("BLOWER MOTOR LOCKOUT -This status code indicates the blower failed to reach 250 RPM or the blower failed to communicate to the variable speed furnace control within 30 seconds after being turned ON in two successive heating cycles."). However, when I turn off and on the furnace power switch it starts and runs fine for a while. Sometimes it runs fine all day, but does not start only once in the evening or in the night. It is 13 years old I was thinking to replace whole thing if repair cost is too high. But I am not ready to pay $10,000. 
PickHVAC Tips: First, see the PickHVAC tip above about sizing a central air conditioner. It applies to heat pumps just as much. Secondly, Even if the line set for the new heat pump is the correct size, we recommend replacing the set or at least the fittings. Old lines and fittings are a major source of leaks. When refrigerant leaks out, the heat pump efficiency suffers. Eventually, the unit stops providing heating and air conditioning, and it might break down.
An alternative to packaged systems is the use of separate indoor and outdoor coils in split systems. Split systems are preferred and widely used worldwide except in North America. In North America, split systems are most often seen in residential applications, but they are gaining popularity in small commercial buildings. The split systems are a great choice for small buildings where ductwork is not feasible or where the space conditioning efficiency is of prime concern [20]. The benefits of ductless air conditioning systems include easy installation, no ductwork, greater zonal control, flexibility of control and quiet operation [21]. In space conditioning, the duct losses can account for 30% of energy consumption [22]. The use of minisplit can result in energy savings in space conditioning as there are no losses associated with ducting.
With the split system, the evaporator coil is connected to a remote condenser unit using refrigerant piping between an indoor and outdoor unit instead of ducting air directly from the outdoor unit. Indoor units with directional vents mount onto walls, suspended from ceilings, or fit into the ceiling. Other indoor units mount inside the ceiling cavity, so that short lengths of duct handle air from the indoor unit to vents or diffusers around the rooms.
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.