I would suggest hooking a proper 10 amp or better trickle charger up to the battery and charging it for a period of 8 to 10 hours. This will charge the battery up to full capacity. Alternators are not designed or capable of charging a completely dead battery in a short time, they will maintain and top up the battery while in normal usage. From your description, all systems sound like they should be working OK other than the dead battery.
1991 M5
Glanschwartz, Black leather,
AC Schintzer Type 1's
Supersprint Exhaust, UUC SS, EAT chip
1989 525iA JSpec