troy400h

2006 400h suddenly would not start. Behaving as having drained battery. Jump start no problems drove half hour to charge battery. Next day same issue. Left town car stayed in heated garage. Car sat for 2 weeks jump started after several minutes. I wanted to take her for a drive and realized shifter was harder to move through all gears and not engaging correctly. With gentle pressure I could get the car to stay in park, drive, or reverse. If no pressure car would suddenly not be in gear and roll down driveway and gear lights on dash will turn off also. Bought a new battery and installed. Shifter is still behaving same. Not sure how charged battery is but car starts as long as I have pressure on shifter to keep it in park. otherwise put car in park alert flashes. Any help greatly appreciated