1995 Windstar GL - Alarm Button kept blinking, Alarm can't be Activated

[JHK]

I have a 95 Ford Windstar GL. It did not come with an alarm system, and I have it installed later. The alarm system is about 9 yrs old now. The front of the remote control has two button "A" (lock car & activate alarm) and "D" (unlock car & shut off alarm). The back reads: Battery Replacement 12V GP23A or Equiv. Made in USA. FCC: GOH-M6101890. DOC: 1409 K791.

Couple days ago, after my dad cleaned the interior, the alarm ceased working. The button/light kept blinking regardless whether the A or D button was pushed. The blinks went away when I started the engine. I knew the alarm wasn't activated, because if it was, there would be two
beeps when I pressed the "A" button. I found out later it's caused by a door not closed tight, the problem was solved when the door was closed properly. A week later (drove twice since), today after I drove the car and ready to park, I realized the alarm button (on the dashboard) kepts blinking after I turned off the engine, and only one beep when I pressed the "A" button (indicate alarm is not activated but doors are locked). I am not sure whether the problem existed before I started the car, I was in a hurry. This time I checked all doors, they are closed properly, assured by the "check door" light not on.

Anyway, now the car can be locked and unlocked by the remote control, but the alarm cannot be activated (I tried opening the door with key while the alarm system is turned on, but no alarming sound goes off). The alarm button on the dashboard kept blinking regardless whether the A or D button is pushed, and would only go away if the engine is started. Does anyone know what is the problem? I just spent 500 to fix the power windows, really can't afford any major repair now. Pls help.