the 2nd time (and only the 2nd time) the battery was nearly dead, the alarm was screaming and even I removed the main battery, the alarm was still screaming and I could do nothing but waited until its back-up battery died too

Hi goodman888

Great looking car!

You've received some sound advice from all of the guys here, but don't be misled by your statement above. Many (most) car alarms IMHO would sound if the main battery runs down low. So that may just be a red herring.
Alos you haven't mentioned if you have fitted a mobile phone, or rather if you have fitted a car kit to mount a mobile/cellular phone.
It is really easy to get permanent live and switched live mixed up and after doing so, the classic symptom is a dead battery after 2-3 days.
This has certainly happened to me a couple of times.

Barry

1994 E200 Wagon 115k miles