Security light

Then immediately attempt to start? I came out this morning to go to class and got in my car. I unlocked it with my key fob and held the button down so the windows would roll down also, which worked fine. I threw my backpack in the back and sat in the driver's seat for a second (probably totaled to about 15-20 seconds before I attempted to start it. All of my gauges and my radio immediately came on, but when I turned the key nothing happened. There was no click or remote attempt by the engine to start up.

Confused, I tried a couple times with no luck. I got out and checked the connections on the battery to the engine, and everything looks good (no corrosion or dirt). I realized that in the time it took me to unlock the car, get in, and attempt to start it, the doors had relocked. Thinking that this may be a security measure for the starter as well, I took my keys out, locked the car, unlocked it again, and then attempted to start it. VOILA! My car starts and has no issues on the drive to school.

I get out of school, and the exact same thing happened. I unlocked the car, took a second to get in, but this time the doors weren't locked. Trying to be inventive, I went ahead and locked the doors again and unlocked it to see if it fixed the problem. Again, it worked and my car started. Now, when I got home, I shut the car off and after about 10 seconds I tried restarting it and it was fine. What's wrong? :(