Does "you can hear the machine running" mean you hear the roar of the burners, or does it mean you hear the circulation pump whirring away?
If the zone relay or (less likely) circulation pump was fried by a power surge it's possible that the burner is coming on, running the boiler's temperature up to it's high-limit, then kicking off until it hits the low-limit temperature (which could take a couple of hours), but for that to happen there has to be power to the burner controls. With no power the internal controls the internal valving to the burners could not normally open on a Burnham series 2, and without power for the high-limit aquastat to interrupt, it would just keep on burning, not a repeated cycling on/off.
In order for the heat to get to the baseboards, there has to be power to the pumps and zone relay, yet it's possible for components to fail such that the burner operates (when powered) without the pump running.
If what you smell is really natural gas, turn the gas valve off where it enters the house and get the gas company or a repair-tech with a sniffer to verify. This is not something a newbie should be attempting to deal with on a DIY basis.