2006 Honda Civic won't start, battery fully charged?

Hello,

I have a 2006 Honda Civic LX 1.8L Engine

Within the last month the car has gotten a new serpentine belt, new radiator, and new ac compressor

I got a new battery in July of 2016.

The morning after the first night it snowed this winter my car wouldn't start, I turned the key on and off 3 times and on the 4th the car started and ran fine. (I assumed the battery was just cold).
The next night I tried to start the car and nothing. The lights and radio turn on but the engine won't turn over, it doesn't even click. It just makes a humming noise like you can hear the battery running.

Even though I know the battery isn't dead, because of the lights, I had a neighbor jump the car, no luck.
Then I pulled the battery out and walked to autozone where they tested the battery, they said it was completely full and worked good.

I'm assuming there is a problem with the starter, but how do I know if it is the actual starter or the solenoid/ some minor problem with the starter that doesn't cost $500 to fix?

Any info on what the issue could be is appreciated!
Thanks

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