First off, how old is that battery? Sometimes when a battery is old, letting it run down to a certain point will no longer allow it to hold a good charge. Or it may just need to be put on a charger for a while. Alternators aren't really designed to recharge batteries from a badly run down state.
Second, since the car hasn't had power in a while, your DME might be in the process of reinitializing itself to the correct parameters, and that can sometimes cause a heavier load on the engine and/or electricals. The rough running could be an indication of this.
Bring the battery to a shop and have them look and see what they can do with it. Let us know how it works out, and welcome to UB.c