1990 Jaguar XJ40 Factory fitted alarm

My Daimler (Jaguar) XJ40 alarm started going off for no apparent reason. This has the effect of opening all the doors, but not the boot. When I start the car the alarm stops. However, after that, the alarm goes off briefly when I start it (4 or 5 seconds). I can no longer use the key fob to open and close the car and have to use the key. The red light on the steering column always used to flash but now it is always on. I was told to disconnect the battery, wait 6 or more minutes and reconnect (I only take the + lead off). This would result in a mewing or mooing sound from the car at which time I should aim and click the key fob 5 times. Unfortunately this didn't work. It just sets the alarm off again. The last time I drove the car the alarm also went off for a few seconds twice during a short journey of about 1 mile. I now have to disconnect the battery every night so that I don't disturb my neighbours but this leaves the car unlocked.

I suspect the battery is not at its best. Can this cause my problem?

Please help, thanks.