Auto security problem? Please help!

I noticed something strange on my car this morning before leaving for work. I own a 2002 Taurus SEL Premium. When I unlock the doors with the
keyless remote, the directional/signal lights comes on and stays on. When I put the key in the ignition to start the car, the car would start, the headlights would come on automatically, but the directional lights would stay on and the speedometer light didn't come on. I tried turning the auto lamp to manual, didn't help. I tried turning the headlights to "off". the directional signal comes off. Tried turning it on again manually, directional signal comes on again. Speedometer light didn't come on. Turned the ignition off, started the car again, same thing happened. The third time, turned the ignition off and started the car, the directional lights came off and stayed off and the speedometer light came on.
When I got to work, I turned the ignition off, got out of the car and locked the doors. Went back to my car during my lunch break, the directional lights came on again and stayed on. I unlocked the door and the directional lights stayed on. Started the car, the directional lights came off and stayed off. When I got back to work from lunch, I turned off the ignition, opened the door and the panic alarm went off with the directional lights blinking. I pressed the panic alarm button off and the lights came off. Pressed the same button again, the directional lights were blinking again. I got out of the car, locked the doors and went back to work.
After work, I went to my car again unlocked the doors and the same thing from this morning happened again. I turned the headlights off, then on, then off, then on, then off, then on again, the directional lights finally came off and stayed off. The speedometer light came on and I was able to drive home safely. By the time I got home, I turned the ignition off, pressed the panic alarm button to see if the directional lights would blink. They didn't blink. The speedometer lights were blinking like they're supposed to with the headlights on. Then, I turned the panic alarm off, got out of the car and locked the door. The directional lights stayed off.
I even checked the bulbs on my car and they were fine. I had my dad check the brake lights for me while I was in the car this morning. They were fine. Could this be a short circuit in the wiring or the auto security system since it was about 21 degrees Fahrenheit outside? Could it be something wrong with the auto security system which I should get the attention of the service dept. at the dealer? I checked everything and don't know where to look. If it is a problem with the auto security system, I should bring it to the dealer and have them look at it. Please help me out by responding immediately with your opinions or suggestion. Thanks.
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