SOS about ABS light!!!

[SHB]

Dear sir/madam:
I am a new owner of BMW 523i A SE, E39, P reg.
I found out there is something wrong with the ABS light inside the dishboard, and I do not know why.

Normal time(Before found that problem): When I put the key in 2nd gear ( The one before start engine) then ASC+T and ABS lights are come out and disappear in one or two sec later. ASC+T and ABS lights will come out and soon disappear after engine has start.

Now(After found that problem): ASC+T light is alright, like normal time. But ABS light is NOT come out after engine start. However when I put the key in 2nd gear ( The one before start engine) then ASC+T and ABS are come out and disappear in one or two sec later(Like noemal time also).

I was pull out the battery from the boot and fully charged before I have a long holiday. Then I left the battry at home(Without charge) while I am in holiday. After 3 or 4 weeks when I came back and put the battery back to my car again, then I found that problem.
So, is that because of the battery have too much power then cause that problem? or something else cause that problem?

However the ABS system is working normaly yet, Whatever the ABS light come out or not after the engine was start.

However the ABS light can come out and soon disappear when I first time to turn on the engine in every day morning.

I've checked all the fuses and top-up the brake oil (DOT 4, BMW made) to the MAX line, but the problem still here.

I took out the battery out of my car and to charge it again a few days ago. Now even more worse, the ASC+T light is NOT working normally too, but better than ABS light, sometimes come out sometimes not, and the ABS light come out only in the morning when I first time turn on my car.

So, could you please tell me why? and how can solve that problem? How about I buy a new BMW battery to replace the old one?
Or some more worse than I can imagine? If so, what kind of serve should I tell to the satff at BMW serves centre?

Please reply by email : sunstorm2046@sina.com

Thank you very much for your patience.