I'm going to attempt to help you out, but i need to ask you a few questions first.
What is the make of the unit? also Model #?
What type of unit is it? (forced air oil or oil boiler)
When the unit tries to start, what happens?
Can you see the flame or feel the flue (exhaust vent) heating up?
(if your going to feel the exhaust vent be very very carefull! when fully heated this pipe can be several hundred degrees)
Ok, i have a hunch that most likely the fuel is not igniting or if it does ignite the cad cell is not sensing the flame.
I have one more question for you, does the honeywell control go into lockout everytime the unit shuts off?
If so here's what i would like you to do.
Hold the reset button in for a full 60 seconds.
Then describe to me everything that happens while the burner starts up. This will help me get a better idea of whats going on in the system.
Ok that something that came on for about twenty seconds, did that sound like a sparking noise?
Also, after that did you hear, almost like a rushing type noise, of the fuel igniting after the spark?
Ok, so then if you had to gues would you say the fuel is probably igniting?
If this is the case, your cadmium cell may have failed or may just be too dirty to sense the flame. The cad cell is in place, so that if no ignition is reached, the system does not continually try and restart. Because every time it tries to restart some fuel is injected into the chamber. If this happens over and over again, then you are at risk for an explosion. If i had to guess, from what you've described to me, i'd have to say that i suspect the cad cell.
I also have one more question to you, are you talking about the air filter or the fuel filter?
The flashing reset button means that the control (probably a honeywell control) has locked out the burner. This is for the reason i mentioned before, continually trying to restart with out ignition is extremely dangerous.
Ok, thats what i thought.
Definately change the air filter if its dirty, this will improve the efficiency of the heating and air conditioning(if installed) systems.
I always recommend this to everyone who has trouble with an oil system: Get it serviced every single year. It is almost guaranteed that you will save money on oil and component failure.
I had a guy who was going through a tank a month, i serviced his boiler system, he has only used 1/2-3/4 of a tank so far this year in 3 months. If i could recommend anything to you it would be to get regular preventive maintenance done on your system.
I hope my answers were helpfull to you!
If you need anything else, feel free to ask!