Classic/Antique Car Repair: Overheating, radiator cores, 1978 chevy impala

Question
I have a 1978 Chevy Impala and lately it's been running hot. I changed out the temperature sensor and the thermastat however, it's still running out.  The water pump is not leaking but when I start the car with radiator cap off, I notice the anterfreez is not circulating or pumping after the car reaches normal temperature. Which tells me something wrong with the water pump.   
What could be the problem?

Answer
Renard, a little more information would help here. Is the car running hot when it is idling or when it is running down the road? Does the temperature increase as you increase road speed? If it does, the radiator cores are probably pretty well clogged up with what I classify as calcium deposits. They restrict the flow of coolant and cause the temperature to increase as you speed up. It is rare that a water pump will not circulate the coolant but it does happen. However the restriction in the flow in the radiator will cause the coolant to look like it is standing still. I would suggest taking the radiator out and letting your friendly local radiator shop take a looksee.
Brad