riello 40 pump?

is there a limit to how many times pressing the restart button will burn out the oil pump???
i recently ran out of oil, got a top up and system was bled. i then had heating for 48hours but then the whole thing cut out and hit the restart button 3 times bit no joy-boiler not firing up. have been told that I have burnt the pump out?!
2weeks before this the heating had cut out totally and only way to start was to hit the restart button twice, no joy, so lower the theromstat and hit restart button and the heating working.
im wondering have i generally by mistake burnt the pump or was it on its way out and me running outa oil didnt help matters???
any info help woul dbe greatly appreciated. in easy no technically terms please as single parent woman and fed up being taken granted for 'repairmen' who charge a fortune for repair bill!!!!