I have a 2007 Camry LE. I have owned this car since 2009. Problems starting lately

when was the last time you replaced your spark plugs?

Not since I bought it. I had someone tell me due to the humming and the fact that it sounded like it was going to turn over that it might be the fuel pump. What does a car sound like when the spark plugs are going bad?

I drove it to work. No problem. Drove home. No problem. Went out to the garage a few hours later, it was humming. Not like a fan spinning but a hum. As soon as I opened the door it went away. The car was completely dead. Replaced battery. It starts again. Runs fine. In the past it ran fine, then suddenly wouldn't turn over. Literally a chugging sound. It was sounding like it would start, would chug a few times (car even shook a little) and then it would quit. After a while it will start. Doesn't do it but a few times in the last few months.

Try popping out your fuel pump relay from under the hood. The next morning put in back in before you leave. See if that cures the dead battery issue. You may have a bad relay that is stuck in the closed position which keeps power running to your fuel pump. Replace your relay. If the car keeps stalling when engine is hot, try replacing your Engine Coolant Temp sensor.

It's probably the fuel pump. I have a 2007 and it did the same thing. I think after driving and turning the engine off, the pump looses its prime. I replaced the fuel pump and it's back driving fine again.