1996 Explorer "Supplemental" Alarm System Problems

I have a 1996 Explorer XLT with what I'm calling a "supplemental" alarm
system installed. It almost looks like an aftermarket install, but as
far as I can tell it's a Ford alarm, since the remote has the FORD
emblem on it. The remote has 2 buttons: ARM and DISARM. There's also
a small red light mounted on the dashboard behind the turn signal
lever, which flashes red, and a separate siren under the hood on the
firewall. The problem: I recently had the car's battery changed, and
ever since then, the supplemental alarm has activated itself (I
originally had it in some sort of valet mode, where I didn't have to
bother with it -- until now). Now every time I shut off the car, even
for a few minutes, I have to press the DISARM button in order to start
the car. I'd just like to know the procedure to get it either
DISABLED, or put back into valet mode so I don't have to deal with it.
There's no mention of this alarm in the owner's manual, and I'm not the
original owner of the car, so I didn't have it installed. Any help
with this would be GREATLY appreciated.

Thanks.