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Here's my situation: I select D and release the brake. The car should start to roll but nothing happens. I need to press the acceleration to make it move. Sometimes the transmission enables quite aggresively, like you know I can make it at 2 k rpm and suddenly - boom - it goes. Rocket launch. Manual car-like start or revving the engine in N position.
The same happens in corners - sometimes I feel that the transmission disables/enables, disables/enables. I need to treat the pedal gently otherwise it may launch unexpectedly.
Have you ever changed your transmission fluid? If not I would do a drain and fill, meaning drain the fluid, measure it and replace it with a slight bit more. Do this 3 times, with 5k miles in between each other.
It sounds like you have a solenoid sticking inside the transmission. More likely from dirty transmission fluid.
When you do your drain n fill, take a small sample with your pinky or clean tissue. examine the fluid and make sure it doesnt smell burned, or super black. It should be maroon in color.
Use only toyota transmission fluid the WS world standard. There have been some who have used amsoil with good success. But the majority we just use the toyota stuff
When you say the problem also happens when turning corners, it could be that the transmission fluid level is low. Cornering allows the filter inlet sucking air instead of a steady inflow if fluid. Are there any leaks? Also check the transmission fluid cooler lines that run to the radiator for leaks.