the rad is just connected to the primarie pipework which will work as you say all the time hw/heating demand.
the water will leave the boiler, go to the pump, then to a motorised valve/s above pump, then the motorised valve will direct the water to what ever is needed hw cylinder or heating or both.
when you call for hw or heating the boiler will fire up
and the pump will run to circulate the water
if the water fails to circulate due to pump or low water content the boiler will activate the overheat stat and go into lockout mode.
when you run boiler feel the flow pipe to the pump is that hot or cold ?
is the pipe from pump hot/cold ?
is the pump fails or the water content is to low then you won't get hw or heating as the hot in the boiler will fail to leave the boiler and go to lockout.
if boiler is firing then shutting down after about 2 mins its not a boiler issue.
9/10 times its a pump failure
hi-spec plumbing & heating (essex)
July 2009