Okay, just so there is no misunderstanding. It is 70 miles (distance) not 70 mph (unless you drive for one hour, then it would be 70 miles distance). I think the previous post (about a week ago) was to show how far he could go on a good battery/bad alternator combo.
You are trying to determine if the alternator or wiring is bad. If the "new" battery holds charge and continues to be charged while being driven, then the "old" battery is the problem. If the "new" battery doesn't hold the charge, then maybe it is the wiring or the alternator.
Of course, if you drive for an even longer period of time and the car is still fine, then it is probably a problem with the "old" battery. Like I said earlier, you may want to put the "old" battery (fully charged) in the trunk with tools so that you don't get stranded if the "new" battery gets completely drained so that you don't get standed by the side of the road.
Incidentally, you probably read that Masscontour posted today that his problem was the negative cable. We can hope that it is the same for you. A cheap fix if you do it yourself.