I have an old furnace, model # ACD603. The oil tank was empty and I had a half of tank delivered. The furnace comes on for approximately 2 minutes then shuts off. I do not think that an oil furnace would have a pilot light. I have to hit the reset button every few minutes for it to start running. Although it starts up, it does not blow warm air through the vents. Any suggestions?

You need to bleed the oil lines to remove the air caused by running out of oil.

If you bleed the line the furnace should work, if not check the oil filter and install a new one. Than bleed lines again.