Q: Car won't start and clicks when the key is turned

Hello - you may have already diagnosed the problem yourself - well done! By that I refer to your comment that if you jiggle or bang on the shifter, it sometimes makes the difference in starting or not. The neutral switch (actually checks for Neutral or Park position), which is part of the shift lever mechanism, is an essential link in the "start" circuit, and may not be making a good connection, preventing you more and more often from starting your engine. It is also possible that it is still the starter solenoid - that is what makes the audible "click" we are all familiar with. I would recommend having a car is not starting inspection completed by a mobile, professional mechanic, such as one from YourMechanic, who will come to your location, confirm this diagnosis, give you an accurate assessment of damage and cost estimate for repairs.