Plugged in, not charging and if I unplug that AC adapter, it turns off

You certainly put a lot more effort into your explanation than Microsoft has to date but I'd like to add:

If your device is at the point where it has absolutely zero ability to be on without a cord connected then you cannot apply the November 2016 fix.  The firmware for the charger inside your unit requires that the Surface Pro 3 must switch to battery power during the install!  So, you may find yourself in the situation where my Surface Pro 3 is, where it retries to install the firmware before every boot.  It goes to about 30% or so and then shuts off.  It tries again after restarting and then shuts off again.  The 3rd reboot it then goes right into Windows 10.

I have one of those that dies whenever power is disconnected.

Then they should replace yours.  Those are the only two I had to get replaced.  

I don't remember how the updates went on them, but I do remember booting being messed up.  I'm trying to forget that dark period in my life.... I had nightmares.... I'm not kidding....

If they try to charge you, don't let them.  

It will be harder to get a free replacement if your device is older and out of warranty.  

Of course, you have to go through their magical steps, that you can find in any search engine, and probably tried a gazillion times... but, you have to do the stupid steps that they email you,  then you email them back.

Day 1:  Send battery report 

Day 1: Replied with battery report

Day 7: Try the steps in this email

Day 7:  I tried and replied that I tried them, again.

Day14:  Oops sorry, your case was closed, call this number....

You get the idea.  It's a long process, but worth it.

Otherwise, every time you look at that Surface, you will have an anxiety attack thinking about Microsoft taking your money then telling you to eff off.... trust me :D

Could you please link to us the exact steps you used that fixed every surface but two?  I would -very- much like to try this set of steps on my surface, which doesn't sound to be as in bad of shape as the two you were reportedly unable to fix.

I have a SP3 with a Simplo battery.

I believe I have tried all of the Microsoft Steps.

Would you please provide the exact steps you used?

I honestly don't remember.  I wasn't kidding about the nightmares.

I do know it wasn't a Microsoft page (their email had a link to a Microsoft help page, but it was very basic.  Run updates and you're good to go)

I gathered different things from different forums over the course of months.

Basically:

As long as your Surface doesn't have any weird "System Hardware Update - 11/7/2016" or two instances of installed (not failed) "System Firmware Update 11/7/2016", you should be able to run updates until you get the System Firmware Update - 11/7/2016.

I am seeing a newer System Firmware Update, dated 1/30/17 on the update history page, but haven't heard anything on it, so i can't comment.

Once you have your updates sorted out (if you do have the weird updates listed above, you will need to reset the device, then update), you need to calibrate the battery.  This is more of a problem than the update, because the battery icon will scare the crap out of you, but you have to follow direction, or it will never calibrate properly.

Power cycle the battery three times:

Let the battery die completely, then charge to a full 100%

Let it die completely a second time, then charge to the full 100%

Let it die completely a third time, charge to the full 100%

DO NOT UNPLUG AT 95% thinking you're okay to use for an hour, then you will charge fully when you can... you HAVE to fully drain/fully charge the battery.

After the update and calibration, the battery reporting will be different.  It will seem to stay fully charged longer than normal, then drop dramatically, then hang around at that percent before dropping dramatically, then it will stay charged all day, even though it says it's at 18%.

It's unsettling, but it's just getting used to the new reporting procedure.

I read (during research on Lithium Ion batteries in general) that we should only plug in when our device tells you to (you can set this percentage in power options advanced settings), and once or twice a month, let it totally die. 

You can track your progress from your battery report:

Open CMD as an admin

Type powercfg /battery report

This will save a file (it tells you where in the command prompt) that may need to be copied to the desktop to open.

Give it a few days to get some data compiled (the updates clears out previous battery activity), but I check the Charge Capacity History.  

You should see a pattern of good to bad to better to good.

After all is said and done, even if the battery percentage is scary, if you're getting an average of 7 hours use out of it (brand new is 9), it's fixed.  Not 7 hours before it drops to 50%, but 7 hours out of a full charge.

Bad memories of clients that refused to let it fully charge are flooding in...... 

I'll be in the corner sucking my thumb.