E63 650i – Electronic problems – battery only?

Good morning together, I am now a few months proud owner of a 650i preface lift. The car is made of serious pre-owned and I could get the noble jewel quite cheaply, because they knew each other personally. He did not have any problems at all, but in the middle of June it started, the water pipe was abruptly down and I had to find a workshop except BMW, which took care of my problem. The car was now standing in mid-June at the workshop of a well-known, which seemed I got the reperature very cheap, that cooling system is now more than dense! But now to my actual problem, if he was standing there almost 2 months, the electronics TOTAL spins! Geared emergency run, DSC failed, ABS failed, sometimes the engine goes off while driving, sometimes nothing is at all and sometimes it only starts again after the 20th start attempt. Can it lie on the battery? The previous owner did last year in winter, before exactly 11 months, get a new battery from BMW, a 90AH battery to be exact. Well, can it be due to the battery? I have this almost exclusively at short distance (time to the tank and back). Well, but the battery was hanging for 3-4 hours at the charger, nevertheless went on the next short distance drive back into the emergency run? The charger was a 4 AMP charger, the battery was once, shortly after I got the car again, completely empty, so really complete, Do you have any ideas?