from what you say I think you have a two pump system one for heating one for hot water when you turn heating one c/h pump comes on and turn hot water on and h.w pump comes on
water in both pumps is the same so yes both can sludge up or burn out,you can test pump by checking if spindle is turning via front chrome nut and check power supply ,however to check inside pump it has to be removed,
water in these pumps is not the same that comes out taps,
cold water in kitchen sink direct from mains
checks also to check if no power to pump check cylinder thermostate and clock output
please note these systems are not used alot now as when heating and hot water on pumps fight each other and can burn each other out
tony...tsp heating, July 2007