There are som many things that you can do. By the sounds of the coffee that was already in the hopper the machine may have had a chequered past.
Firstly, use a Jura cleaning tablet (or 2) in the cleaning cycle to clean the brewer internally maing a cleaner brewing surface. If you dont have any they are available from here (http://www.gilkatho.com.au/shop/Scripts/prodView.asp?idproduct=40).
Secondly, look in setup and adjust the Powder Quantity to give yourself a better shot.
Thirdly, adjust the grinder while it is in motion and try 2-3 coffees in each position before moving onto another position.
Fourthly, is there a water filter in the water tank? If the age of the filter is not known then I suggest replacing or removing it. Once the filters have expired they are no longer filtering the water anyway and may just be retaining old tastes & odours.
Let us know the feedback from these and we can guide you further.