MacBook Pro immediately shuts down when disconnected from charger, auto starts when opening MacBook, even after shutdown I am running macOS 10.14.6 on a late 2013 MacBook Pro.  The system immediately shuts down when the charger is unplugged.  Oddly, even after intentionally shutting down the computer, it auto-starts when I open the lid.  

I reset the PRAM and SMC, which didn't help.

This began several weeks ago when the system shut down for no apparent reason.  When I restarted, the system date was way off.  I reset it to auto detect the date. I could still operate under battery power, but it would shut down long before the battery was drained.  

Now it will not operate on the battery at all.  After this random shutdown the battery condition was displaying Replace Soon. Now it displays Replace Now.  Cycle count is 194.  System information shows that the battery is not charging, even though plugged in.  For several months now I have noticed that the case will sometimes get very hot to the touch above the keyboard at times.  I installed Macs Fan Control and verified both fans are working properly.

How can I resolve this problem?
Your battery is old even if it still has a low cycle count. You might even have a battery that has been damaged in production. In all cases you should not continue using your MacBook in this condition. The battery could start producing gases, inflating and destroy it in the process.