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.
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. 
As you can see, if we know what the contractor is actually paying for specific equipment, we know what their labor rates are, and we know what they bid the project for, then we can also use some basic algebra (or just let the program do it for us because we’re lazy) to figure out how much of a profit they are making off of us (you) at different bid prices:
Fast forward 1 year and 1 week and the circuit board that HVAC Service had installed has failed again. They came out and said that it failed from water condensation dripping onto it, so we needed to replace it and reroute the pipes to prevent future water damage.  That would cost double what I paid last year.  Why didn't they fix the problem last year at the initial repair instead of putting in a circuit board that was bound to fail again?!? They were strongly recommending that the furnace be completely replace for a huge fee to avoid the same thing happening again.  I paid $59 for them to tell me they didn't fix it right last year. This didn't feel right, so I sought a second opinion.
If you hear clicking that is followed by a hum or buzz, you’re probably hearing the fan motor attempting to start without the boost it needs from the capacitor. You can almost always conclude that the capacitor has failed. Sometimes you can get the compressor fan spinning (clockwise) by pushing it with a thin stick or long screwdriver poked through the grille. But the chances are good that this might work for one cycle, but the capacitor will fail next time the AC goes on. It’s best to replace the capacitor.