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).

At the state level the rebates are still substantial. For example, switching to a zoned system can get you a $100 rebate from various A/C companies, and state rebates are also included. In Pennsylvania a high-efficiency air conditioner alone can get you up to $300, and a high-efficiency complete HVAC system can see up to $1000. Maryland's incentives get up to $1,250, with a $100 rebate on a tune up of an existing system.
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. 
Ductwork pinging or popping. If you hear a pinging or popping sound coming from metal ductwork, this may be caused by thermal expansion or by air blowing past a loose flap of metal. Track along the duct runs, listening for the sound. If you find it, make a small dent in the sheet metal to provide a more rigid surface that’s less likely to move as it heats and cools.

We divided new HVAC installation cost into three groups: first, the Change-Out, which is an installation of just your HVAC components without the ductwork; Full Installation, which is the installation of all HVAC equipment including ductwork; and finally, Full Installation with Features, which is a full installation with additional features such as a zoning system or media filter with a complimentary Ferrari Portofino.
7 To test it, turn the thermostat to OFF, reset the power at the disconnect next to the compressor and the main panel. Set the thermostat to a temperature below the room temperature, and then switch it ON. To avoid straining an air conditioner’s compressor, wait at least five minutes between turning it off at the thermostat and turning it back on. You should hear the outdoor compressor run and see the fan turning inside the top. If the fan isn’t turning, look for an overload button or switch to reset (not all types have this).
Central, "all-air" air-conditioning systems (or package systems) with a combined outdoor condenser/evaporator unit are often installed in North American residences, offices, and public buildings, but are difficult to retrofit (install in a building that was not designed to receive it) because of the bulky air ducts required. (Minisplit ductless systems are used in these situations.) Outside of North America, packaged systems are only used in limited applications involving large indoor space such as stadiums, theatres or exhibition halls.

Whether or not central air adds value to your home depends on your location. You probably won't recoup the entire cost for the installation, as it is an expensive project that isn't as flashy as something like a new deck. But this invisible upgrade can help you sell your home if you live in a hot climate. And many buyers are willing to pay a bit more for a working AC.
I originally took off one star because of the SNAFU with getting the part ordered.  When Alberto called me on the phone he admitted the person had "gotten busy with other things" and apologized.  THAT was taking the high road and I was impressed by that.  Sadly, for reasons I won't guess at, Alberto has decided to take the low road in his comments and imply that they got the part as quickly as possible.  Well, we called at 2:30 so did someone spend six and a half hours finding the part??  That seems very doubtful.
The use of furnaces, space heaters, and boilers as a method of indoor heating could result in incomplete combustion and the emission of carbon monoxide, nitrogen oxides, formaldehyde, volatile organic compounds, and other combustion byproducts. Incomplete combustion occurs when there is insufficient oxygen; the inputs are fuels containing various contaminants and the outputs are harmful byproducts, most dangerously carbon monoxide, which is a tasteless and odorless gas with serious adverse health effects.[14]
In addition to the information below, see these two articles for the general care and maintenance of your air conditioner: Preparing Your Air Conditioner for Summer and How to Replace Furnace & AC Filters. Most noteworthy, you should replace the filters at least twice a year, before the heating and cooling seasons. For information on furnace problems, please see Furnace Not Working.