Avalon doesn't start

[Jack Hagedorn]

I own a 2014 Toyota Avalon hybrid. In November (its now February), I got a no key message on the dash and the car wouldn't start. I drove it directly to the dealer and he tested the starting Battery and said that while it tested good it was 5 years old and was probably the problem.  Three weeks later, when I had the problem again, I brought it to the dealer and he said it was probably the aftermarket car starter.  After hesitating  another week or so, I had them take the car starter off at my expense. This was in January. It is now February 24, and last Saturday the car wouldn't start again. It's acting like I have no key fob. I have replaced both key fob batteries in December and in early January the car wouldn't start when I had both fobs in the car. I am at a loss as to what to do.  Any suggestions?