start as a flooded engine for 97 corolla, why and how to fix on 1997 Toyota Corolla

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My 97 Toyota Corolla (136K) can start only if following the instruction, described in the manual, for a flooded engine: turn the key to ignition and push the gas pedal the same time for ~ 5 seconds, release both, then start the car. Sometimes, have to repeat several times.

It seems the problem started this summer, but was minor. After I changed engine oil(5W30, new england area) and filter last weekend (I have been doing this for the past 10 years), the problem came out on a wet Monday morning. I thought the battery died out, then got a new one. The problem is the same.

I am the original owner, and the car has never been in water. The scheduled maintenances were done before 50K. Except for regular oil exchange, no any other service was done after 50K.

I love this car, but just afraid to take the car to any garage because I have been ripped at least twice by the dears (they once charged me ~$250 for a spark plug replacement on my other car!). Can somebody explain to me why this happens? How to fix it? Many thanks in advance!
(1) Answer
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Really, the best thing to do is to have a good diagnostic tech scan your data stream while the car is cranking and being difficult to start. There are so many things that it could be that the best thing is to check for the ignition signals on the scanner and then the fuel signals. The tech should try to find what is missing. And, of course, check for any and all stored codes.
thanks, Dandd!
I did the diagnostic using a code scanner(pocket one, bought from Autozone) while the car is running. Nothing is shown up!