2002 Kia Optima Car won't turn over

There are a few things that happened with the car, and so I think it is best that I explain those first. First, I was replacing the factory radio in my car to an after-market stereo. I had the lights on, but it was also during a snowstorm and very cold. It was too cold, so I came inside. The car would not start. I tried to jump it myself, but it would not start. Thinking that it could possibly be the battery, I called triple A to see if they could jump it. The car would not jump, and the AAA guy indicated that it was probably the starter.

Within this time, the door lock got stuck due to the cold. It was probably -5, and I could not shut the door, so it remained bungee corded until it warmed up and I was able to fix the problem. By then however, the battery was completely drained.

Fast forward a week, and I was finally able to buy the starter. I lifted the car, took out the old starter, and put in the new starter. The car would still not turn over and was making a clicking sound. I knew this was because the battery, so we tried to jump it, but I believe the battery was completely dead.

I went and bought a new battery. Now the car is not clicking, but it won't turn over. I know it wants to start.

I'm starting to believe it may be the starter solenoid? At this point I'm lost, and not sure what I should look at next.