About a week ago we had a cold spell where the high was about 0 degrees. On the second day my battery died and I had to get a new one. Ever since when I lock my car (03 wrx stock security system) with the remote it beeps three times like when there is a door open. Now when I open my doors I do see the light on the dash for a open door. When I close the door that goes away. I thought maybe one of my door ajar sensors was bad but wouldn't the light stay on all the time then? Also my car like randomly went into valet mode the other day and then went off after about five minutes of driving. I'm stumped to what is going on.