Gas and Oil Home Heating Furnaces - Having to push ignition button all the time

I have recently purchased a home with an old wesco oil furnace with an outdated honeywell stack box on it. It started getting cold and noticed it was not kicking on in any fashion, without pushing the ignition relay button on the stack box...conventional thinking (or so I thought) change the original thermostat (and i do mean original..1960's maybe)..had four wires.. 2 coming from what I guess is the low voltage relay, a red and green, then 2 returning from the t-stat to the honeywell box (inside to the ignition relay) white and black. I put the new t-stat on and it worked!..a day later same problem!!! I checked the voltage coming down from the thermostat going to the ignition relay...one wire..24-27 volts..the other 5-6 volts. After beating myself senseless I woke up one morning to the furnace working fine!!!...it lasted for about 4 days then back to the wont fire by itself. The furnace fires perfectly after pushing the ignition button...blower operates after temp rises a bit, and furnace shuts off when t-stat setting is fulfilled. Any advice is REALLY appreciated.

Hi bryan:

Be careful about getting too much oil vapor in the combustion chamber. Pull the stack switch out of the flue pipe and see if the helix is sooted up.

Ok, I did exactly that and found that it was horribly sooted up, cleaned it up best I could, furnace started...stopped abrubtly(no blower delay as the furnace cooled down and t-stat not satisfied) and will not fire up at all now...not even pressing the ignition button. Motor reset button did not trip and voltage still appropriate from t-stat...found 115 volts inside honeywell box...now what did I do and or cause!?!? Hopefully someone can point me correctly as I have called 13 places to no avail for service and the 2 I found can't come out for days...its in the 40's outside, so hopefully I get a response or 2 soon. ( And yes I know...its time to upgrade the unit but, cant do till summer)

Well after tinkering with the relays I found that for whatever reason the recycle relay timer was stuck...after giving it a good wack with the screwdriver the furnace came to life...checked the on and off via the the t-stat and so far so good...Thanx DaddyJohn :) Your response was/is much appreciated