When the coolant goes out and gets low, the boiling can push the water to the top of the radiator like you saw. The system is really out of water and your sensor has no hot water on it and does not always read hot or overheated. Driving on can cause the crankshaft and connecting rod bearings to fail because the extreme over temp of your engine caused the lube oil to become too thin to provide adequate lubrication. Basically, you 'cooked' your engine.
What should have happened was to let the car sit until it cooled down completely, then add coolant back to the proper level after you did the hose repair. Start it and let it warm, then recheck the level of coolant, it will usually change and need more.How do you know the water pump on your car is gone out?I suspect a pocket of air is trapped in the upper portion of your cooling system.
When your radiator hose broke, you obviously lost most if not all of your coolant.
When the coolant was replaced, you now possibly have an air pocket inside your engine. There should be an air bleeder valve near the top of your engine cooling system.
Open this valve slightly to allow the trapped air to escape. Close the valve when coolant comes out of the valve. If no coolant comes out, add more coolant to the cooling system until coolant comes out of the bleeder valve. Then close the valve. Repeat this process after a few days.
Signs of a bad water pump.
Overheating obviously
Coolant leaking from the water pump.
With the engine off, see if you can rock the water pump pulley from side to side. If you can rock the pulley from side to side, the water pump bearings are worn out or damaged and the pump needs to be replaced.How do you know the water pump on your car is gone out?yes it is the water pump. change it and have the whole system flushed