what Im reading is pretty normal operation, the oil lamp will flicker as you crank the engine because the starter sucks about 300 amps from the battery when starting the engine.
even if the engine does not fire, the 200 or so whatever rpm the engine was spinning to get started was rotating the oil pump and filling the pressure galleries and the oil lamp may go out even while cranking for a long time.
Your problem sounds like a long starting period - not oil light problem.