have you got a multimeter with ohms on? Test pump for resistance? If its open circuit its probably dud. If you haven't got a multimeter. Turn off pump, undo cap nut and give impeller a spin. Replace cap nut and try pump. Don't forget most pumps have induction motors and will hum without turning the impeller, unless of course its burnt itself out. Try feeling the hot flow coming from the boiler to the pump, if its hot and the delivery side of the pump outlet is hot well past the pump, the chances are the pump is working but the system may be full of sludge.
If you do find its full of sludge, drain and refill it at least two or three times, do two hot flushes and a cold, adding fernox or similar to keep the system clean.
Its unusual actually you usually find out a system is sludged up in the autumn when you first start it up after a long period of lay off during the summer, that is why its probably favourite to think in terms of a failed pump.
But why not do it all anyway?