"Greg O" wrote in First off,

QUIT PUSHING THE BUTTON!!.
If the pump is working all she is doing is flooding the fire box with oil!

It may be any one of a bunch of things. If it trips off it is because it
is probably not firing. No oil in the tank, bad pump, no spark, bad cad
cell, bad electrodes, improperly adjusted electrodes, broken pump drive,
and probably a dozen more I cannot remember right now!
time to call someone!
Greg

Greg hit on all of the causes, and yes! STOP HITTING THE RESET!! When
someone comes out to fix it, TELL them you hit the reset a bunch of times!!
They may have to soak up some of the oil and then burn off the excess.

If the boiler is cold, that can cause some of the gaskets/seals to loosen up
thus the water drip.

If she can live with a cold shower tonight (tell her to come by your place
for a shower...;-] ), tell her to call someone out tomorrow. Have then go
ahead and do a "clean and service" while they are there. That way she'll
have it "up to par" for the winter....