The issues you are having with the thumping and the flat battery are probably not related. The E-28 body style is a very robust model and one of my favorite cars. As to the thumping noise, it sounds like the drive shaft has a failed center support bearing. At the mileage you stated ,i would recommend replacement with a remanufactured or a new unit from BMW. A remanned unit can be obtained from Oceanside drive line in north San Diego county. Or a new unit from "realoem.com" which is an online supplier of BMW parts. The flat battery should be addressed as a separate issue, start with placing the battery on a charger and bring it to a full charge. Then test the charging system for proper output. Then test for any parasitic draw(AKA key off draw) This should rectify(ha ha) the problem. Please repost to me if more assistance is needed.