Alarm Troubles

I just purchased my 97 Supra a couple of weeks ago. I went out to get in it last night and it would unlock and lock right back. I tried opening the door after a few unsuccessful attmepts with the keyless entry. The alarm started going off. Nothing I did with the keyless entry would shut it off. I finally got inside the car and put the key in the ignition. That shut the alarm off. Now when I go to arm or disarm the alarm it does it's normal routine and locks, lights flash, but no horn. I also noticed that the little red security light down by the window remote is always on.

I've tried to reset the alarm with my keys but it will not even let me lock the car with the key, just unlock. I disconnected the batter for about 15 minutes and reconnected it. No change. I'm out of ideas other than to take it to get somebody to look at it. I know there is an easy fix, but I am lost. Any help, suggestions, ideas would be very appreciated. Thanks in advance.

-Ryan