The most likely cause of a "no cooling" problem is no refrigerant in the system. If the refrigerant has escaped past a leaky compressor or O-ring seal, leaked out of a pinhole in the evaporator or condenser, or seeped out through a leaky hose, the leak needs to be identified and repaired before the system is recharged.
One of the first things you should check, therefore, is compressor engagement. If the compressor’s magnetic clutch is not engaging when the A/C is turned on, the problem may be a blown fuse or a wiring problem. If the fuse is blown, replacing it may restore cooling temporarily. But the underlying reason for the fuse blowing in the first place needs to be identified and corrected to prevent the same thing from happening again.
All vehicles leak some refrigerant past seals and through microscopic pores in hoses. The older the vehicle, the higher the rate of seepage. Newer vehicles have better seals and barrier style hoses so typically leak less than a few tenths of an ounce of refrigerant a year. But system capacities also tend to be smaller on newer vehicles, so any loss of refrigerant will have more of an adverse effect on cooling performance.
Leaks can be found by adding special dye to the system (available in pressurized cans premixed with refrigerant), an electronic leak detector, or plain old soapy water (spray on hose connections and watch for bubbles -- requires adding some refrierant to system first and turning the A/C on). Once you've found a leak, repairs should be made prior to fully recharging the system. Most leak repairs involve replacing O-rings, seals or hoses. But if the evaporator or condenser are leaking, repairs can be expensive.
An A/C system that blows cold air for awhile then warm air is probably freezing up. This can be caused by air and moisture in the system that allows ice to form and block the orifice tube.
Evacuating the system with a vacuum pump will purge it of unwanted air and moisture. Evacuation should be done with a vacuum pump that is capable of achieving and holding a high vacuum (29 inches) for at least 30 to 45 minutes.
For best performance, an A/C system should contain less than 2% air by weight. For every 1% increase in the amount of air that displaces refrigerant in the system, there will be a corresponding drop of about one degree in cooling performance. More than 6% air can cause a very noticeable drop in cooling performance, and possibly cause evaporator freeze-up.
Noise from the compressor usually means the compressor is on its way out. But noise can also be caused by cross-contaminated refrigerant (operating pressure too high), air in the system or the wrong type of compressor lubricant.
Noise can also be caused by hoses or other parts rattling against other components in the engine compartment. Check the routing of the hoses, support brackets, etc., to pinpoint the noise.
If a vehicle’s air conditioner blows out air that smells like the inside of old gym sneaker when the A/C is turned on, microbes are growing on the evaporator. Mold likes damp, dark places. Bacteria can also thrive under such conditions. Besides smelling bad, it can be unhealthy to breathe (ever hear of Legionnaires Disease?).
To get rid of the unwanted organisms, various chemicals can be sprayed on the evaporator directly or through the blower ducts or air intake. Many replacement evaporators have a special chemical coating that inhibits the growth of mold and bacteria. The drainage tubes that carry condensation away from the evaporator should also be inspected and cleaned.