I assume the header tank is at a low level which means the pressure is too low to fill the rads - a common problem.
If the pump is fitted in the return side of the system, and the rad valves are screwed down, it is possible the pump may suck water away from the rads resulting in the situation you describe.
Turn the pump off and bleed. What happens?
If that doesn't work a neat trick is to firstly work out which end of the rad is the feed (gets hot first). The turn off the return end valve and open fully the feed end - then bleed again. The pump should then be forcing water into the rad.
I wouldn't have expected this to damage the pump. Only if pumps are allowed to totally run dry for a length of time will there be a problem. They overheat and the bearings wear.
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