Oil furnace stopped running and reset button on furnace doesn't work. What do I do?

Actually you should call for professional for on site service to repair/tune up your burner. Oil furnaces/burners should be tuned up every year and that type of work is usually impossible for a home owner to do. A burner that is not properly tuned and adjusted uses more oil than a burner that is running correctly. So in some respects a good quality service actually saves you money since you will be using less oil to heat your home.

I am sure you already checked this but do you have oil in the tank?