Why did my refrigerator/freezer stop cooling?
It sounds like there can only be 2 causes for the failure. 


The compressor is running inefficiently (normally caused by blow by or a bad winding on the compressor) -
The only way to know of this is to hook a set of gauges up to the system to see the High and Low side pressures, and to check the resistance of the Run, Start, and Common windings of the compressor.
There is a leak in the system (Normally very hard to find in fridges)
The only way to know this is to hook up a set of gauges to the system. In order to find a leak in a fridge i would use an electronic leak tester as it can get into very confined spaces. The other way to find a leak would be to pressurize the system with nitrogen, and try to hear for leaks. If there is a very small leak you will have to go around with soap and water, or a type of refrigerant leak detector. The unit is more likely to leak on the high side of the system due to higher pressures and tempratures. This would be from the discharge of the compressor to the metering device, or the inlet of the evaporator. Other common places or leaks would be, the evaporator coil, or the condensing coil, along with any joints there may be in the system.


If the system just suffered a leak, and there is no damage to the compressor. If the leak is easily identified and repaired, the system can be recharged and repaired for a few hundred dollars. However this is normally not the case with leaks. If there is a small leak it can take hours to find and repair. Also if the leak is in the condenser or the evaporator, a replacement and the cost to replace it would normally cost about the price as a new fridge. The same goes for a compressor issue. If the compressor is running inefficiently, and must be replaces, the cost of the replacement compressor, the labor to replace it, and the refrigerant to recharge the system would also normally cost more then the price of a new fridge. 

If you are going to have it repaired, have it done by an Appliance Repair Technician or a Refrigeration Technician.