04 corolla. Oil light comes on. Full of oil.

Oil light is rather important it goes out if oil pressure is good comes on if oil pressure is low when it comes on damage is expected with continued operation like wearing of main bearings and pistons and cylinders can lead to a engine rebuild

check that you have put the right amount of oil in the sump as the oil light is probably coming as the oil surges away from the pump. disregard the dip stick for a minute . There is normally around 4 litres of oil in a sump ( 1 us gallon)

The oil light will come on with low oil pressure (it is most likely a faulty / blocked sensor). This could be a simple sensor fault or blocked pick-up or a problem with your pump. I would get it checked out - if the oil pick-up needs to be replaced or cleaned the sump would need to be removed. A quick visual is to open where you top up the oil and see if you can see no oil at the top of your engine if there is very little or none then it is definitely the pick-up and don't drive the car as you will cause wear. If you start your engine you should see oil "sloshing" in the top end - again if there is none then there is no lubrication for the top end.

Possible oil pump, or oil pressure sending unit.

Not saying that this is your problem but it might be your oil pump is getting weak or your oil pickup is dirty. I would start by changing the oil and filter.

Have an oil pressure test done. That requires a mechanical oil pressure gauge attached to engine. These are notorious for oil pump wearing out due to improper oil change techniques. Attached is note from Rover service manual;

Oil filter renewal

NOTE: To avoid draining the oil pump, it is essential that the engine is filled with oil to the correct level, before the filter is removed. It is therefore recommended that the engine oil is renewed before work on the filter commences.

Replace the oil pressure sender. The sender is what is turning the warning light on.If you replace the oil pressure sender it should fix the flickering light problem. If it does not , the light is an indication of more serious motor killing problem. Fortunately, the sender is under $10 and usually fails before the actual oil pump.

other reasons:

perhaps it has too much oil in it? is it right on the fullmark, or above?

solution - drain some out by carefully undoing the sump bolt and holding it so only a dribble comes out, its usually one litre between E and F on your dipstick.

check your motor belts(fan, alternator, aircon) have any fallen off or are loose, some cars have vacuum pumps powered by the belts that maintain oil compression in the engine.

poor compression in your cylinders perhaps, symptoms of a worn motor
get a engine compression test done.

your oil pump may be getting wornout, this is a pump within the engine that pumps the oil from the bottom back upto the top so your motor is properly lubricated, no real way of testing this, try replacing this as a last resort, its usually cheaper to put a 2nd hand replacement motor in.

Do whatever the owner's manual says. Full synthetic is better than a blend, it's all a matter of how much you want to pay.

well the oil sending unit is located on top of the oil filter housing most likely its bad if not your knock sensor is bad