Take the starter down to a place that checks them for free? all to often it can be the starter.. I've seen a a bad starter kill a new battery to usless ( and I mean needing replacement) overnight! but start the car the morning before.You can get some indication of the problem by turning on the head lights and starting the car on the battery at full charge. The lights will dim if its a bad starter or one of the cables is grounded by being burned up against the manifold, etc and the cable(s ) will get hot to the touch.