MAD SCIENTIST MODE --- READ AND EXERCISE INSTRUCTIONS AT YOUR OWN RISK
I stopped reading at your first paragraph since I'm certain I know what to do! ;U (I am replying ASAP for your convenience, DW I'll read. ;3 )
You are correct, batteries, the Lithium ones have a chip on them. When they're depleted to 0 and left too long, the trigger in this chip will say the battery is dead, and will refuse charge.
Can it be fixed? Nnnooooooo.... YES! With a little science. ;d
V = I / R
Which means.. Volts equals Current over Resistance.
Why is this relevant? Here's the trick..
These three things with power are wondrous and magic.. and the key thing to look at is resistance. When Resistance is introduced to Heat.. Resistance will begin to rise. When Resistance rises, and is multiplied with Current.. the Voltage increases.. INSIDE THE BATTERY! 😄
So because the chip on the battery will no longer accept charge.. thinking the battery is dead, if you heat the battery up, which will increase the Resistance, then will increase the Voltage, you will TRICK the chip into thinking the battery is alive again! IT'S ALIIIIVE!!
So what do you do..?
IF you're out of warranty.. pull the laptop apart, find the battery.. if you can unplug it, good. Then, use a hair dryer and heat it up to say.. 45*C? 50? . Do not get it too hot or it'll of course.. do bad things... like.. explode. :f
When hot enough, (not too hot to touch) insert it back into the laptop as soon as possible and charge it.
You will have fixed your battery.
Have I done this? Yes. But not on a laptop, on an iPhone I have though, and it worked.
Don't let the battery ever die again, they should never drop below 20% and if they do, you charge instantly.. and after doing this exercise.. never use your laptop off wall charger.
P.S. the reason your compy keeps turning off is because it needs the battery's power too to supply the unit with enough power to run. ;x