When I turn on the central air, it starts and runs fine. I have a programmable thermo. Set at 73 degrees. The problem is this, when it reaches it temp setting it turns off. However when the inside temp rises above the set temp the system turns on, but the part of the a.c. unit that pumps cold air(compressor, sound like a refrig?) does not come on. The fan is turning on a.c. but no cold air is present. After 4-5 hours of this finally the compressor turns on, I can hear it buzzing and the cold air is once again being introduced into the house.

What is the temp rise over the 4-5 hours the compressor is not running?

4-7 or so degrees, and no it never becomes uncomfortable in the house.

Some condenser units have a time delay to prevent the compressor from starting up for five or so minutes after the last call for cool, or during a short power outage. This basically keeps the compressor from turning on for about five minutes after the compressor shut down. Saves on the compressor for sure. However, these devices have been known to fail. I would check to see if you have a time delay in the condenser, or even in the furnace. I would have to say that your best bet would be to call in a service tech, as there are actually quite a few things that can cause this.

I don't know where you live but in the summer, if your house is only going up 1-2 degrees an hour without AC, you are in a very cold climate or your AC is working. It may be switching out with a thermal overload or a pitted contactor. I live in ATL and I promise you even with a new, well insulated house, at 90 degrees, the house would go up a lot more than 1-2 per hour. Is the compressor in full sun? Have you gone outside to see if the condenser fan is running?