No Heating or Hot Water

I have just reconnected put my radiators back on the walls after some refurbishment and have no heating or hot water. When the central heating comes on the boiler fires up for about 2-10 seconds then turns off again. The immersion heater is upstairs and there is a pump next to it which I checked and it is rather hot and making a loud vibrating sound. It is a combination boiler about 2 years old but I have only been in the house 6 months. I have bled all the radiators.

Any advice please?
Many thanks

Sure it's a combi? with an immersion? take the chrome plug out of the middle of the pump to expose the rotor. See if the rotor goes round (push a scewdriver blade against the rotor when the system is on and hear the scraping noise, sometimes there's a slot in the end of the rotor so you can turn the rotor with the screwdriver to free it). If the pump is powered up but still doesn't spin after this, change it.