Car doors locking, unlocking, flashing headlights, trunk popping open, dome light staying on without car being on. Tried jump starting car, but won't start.

Did you buy it from Linda Blair? Is it parked on Elm Street? It sounds possessed. --- Disconnect the battery. Charge the battery for at least twelve hours to get a full charge. Hook the battery back up. -- All those functions are controlled by the BCM (Body Control Module) and it could be damaged.

I agree tenspeed. The same thing happend to my neighbors Jeep Liberty and it turned out to be theb BCM.

Do you have an aftermarket remote starter? If so, 1st place to begin. These are notorious for failure and are often installed poorly. Next I would look at both batt terminals and batt connections followed by main fuse block left side of dash. Look for corrosion and repair if any found. BCM is next suspect.