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So far it sounds like you may have run out of oil and there may be air trapped in the fuel line or the pump in the burner..... or that there was sludge in the bottom of the oil tank that got stirred up when refilling the tank an the sludge has fouled the pump.
Tell me if any of that might apply in your case or not please.
Next I need the brand an model number of the oil burner assembly so that I can send you maintenance instructions on it.
We can go from there.