car won't start, no cranking of starter ,let sit, comes right back, full battery

When this problem 'acts up' I would check to see that you are getting 12 volts to the trigger wire on the starter solenoid. You may need 2 people to check this. If so, then it is most likely a defective starter, if not then it could be a defective ignition switch, neutral safety switch etc. As for the stuck in park, make sure that your brake lights are working when this happens, because the shift lever release solenoid is cued from the brake light switch. Hope that these suggestions give you some things to consider.