What does it mean when radiator cold and engine run hot?

It means that the coolant is not circulating. Either from a lack of coolant, a stuck thermostat, a failed water pump, etc.

**The water path from the radiator to the engine is blocked somehow. First look at your thermostat. This devise will regulate your water intake into the engine, if it is weak or gone bad, it will not work properly to regulate your cooling system. Check your hoses too, they can collaps and cause no water to flow. Then there is your water pump to check.