Window AC not cooling
See: 
http://homerepair.about.com/od/heatingcoolingrepair/ss/wind_ac_troubl.htm
or
Try searching the internet for "repair air conditioner" or "appliance repair,"  or "window air conditioner repair."

If the compressor starts, but then shuts off, it may be overheating, caused by a blocked tube.  A thermal overload device cuts off the electricity to the motor.  When it cools down enough, it will close again (like a thermostat) and allow the compressor to run again until it overheats again.

If the tube is leaking, it will blow bubbles (even very slowly) when you apply soapy solution on the tube where you think it is leaking. If the refrigerant gas has completely leaked out, it may not blow any bubbles. If the compressor will not run, it will not pressurize the refrigerant gas to force it out through the leak.

When the compressor does not start at all, you may still hear a humming sound, which means that electricity is running through the coils in the compressor motor, but it won't rotate.  This can be caused by a faulty starter capacitor.  The purpose of this capacitor is to allow the starter coil to "kick" the coils out of magnetic alignment and allow the running coils to take over.  Turn it off right away to prevent overheating. 

I replaced a capacitor in one of my air conditioners, and it worked again.