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.
That being said, I'm guessing it has something to do with the key fob not relaying to the ignition that the car has been unlocked (at least that's my guess, and be easy on me if this is wrong b/c I do not know that much about vehicles). If this is the case, how do I fix it and how much would it cost?
I'm hoping it's something simple like a fuse & I can get some good news. Thanks in advance for the help!