I have a 2006 Toyota Avalon lmt with push start with approximately 190k miles. So for starter I had to leave the car parked for a month and went to jump start it one day and started right up no problem with the key fob. The next day I try to jump it so my mechanic can tow it and it wouldn't start. When I press the brake the push button light up green but won't start when I press it also I have the engine immobilizer light blinking. I've tried the 4/13 pin reset, I've checked the starter relay and it has continuity Ive tries the battery removal Ive tries to drain the car with the cable trick by leaving the cables touching without the battery in. I don't know what else to do. The fob locks and unlocks the car also.
Do you have another key to try? The fact that the immobilizer light is blinking suggests that the key does not communicate with the car computer.