that PC is 6 years old, it is not new, my guess you bought it used, or refurbed (means dusted off)
my guess is the main battery is bad, remove it and test with no main battery now, it will run on AC pack endlessly, I do all the time. (expected too)
your SSD is ok, it must be windows 10 on it? why post lacking the key facts like this, windows what, (just one I have is Linux)
and w10 it loves to scramble the boot files. when things go wrong.
the fix was easy is you had asked then, (turn fast boot off)
that normal disk must be used right?, you never said....
the windows 10 if it BSOD's then saves (silly no) the image of the OS running in Memory, this magic is called, fast boot.
turn off fast boot on that SSD and bingo it works.
the other fix for the SSD (amazing 2 fixes. no?_) of 3.
is to power on the PC with SSD , and hammer the HP F11 key
that is the magical HP recover key that reloads w10.
we have 5 HP 8540w in the family here, all with added W10
all with SSD added, all 5 scream .
This PC you HAVE, HP supports XP to W10
32 and 64bit, 5 versions there, a fact see HP link.
you bought a used PC.
my guess, the seller put the SSD there,
and now the HP F11 key is dead,
the seller put on w10 neat, so that all HP software is missing now.
there are 2 problems here, one is maybe bad memory card.
when that happens W10 BSODs all do, every one.
then W10 OS is corrupted, the fix is here.
W10 deleted the F8 key (see how telling what OS this is matters)
they changed how to get to SAFE mode, that was your first.
step, with any SSD the fails to boot.
SAFE BOOT confuses so many folks, but can be turned off
ASK HOW, and is FIRST !
on mine I hammer F11 and go to blue screen #3 here
http://www.pcdied.com/BSOD-s/W10-DEAD.html
when you go to real safe mode,
you then exit windows and the boot files now work
if the memory is not bad, that is.
the books are still there,.. see em? see no SSD there, !?
https://support.hp.com/us-en/product/hp-elitebook-8570p-notebook-pc/5212912/manuals
this is my best answer lacking what OS is there
nor any service tag data,, lots of options on this high end model.
and best docs of any PC made, why I own 5. (i gift them. to fam)
BSOD 101.
can be just overheated, if you block the vents on mine
it overheats fast, for sure I7 processor , is it
my i5 run way cooler.
the fan has radiator on the left side if it packs in lent
this PC overheats fast... all do, every one.
we clean it every 6 months with CAN-O-Air
seen in walmart (shelf next to camera dept)
blow out all that lent or I promise you it will overheat.
all do this ERA of faster PC laptops.
on mine it processor and gpu suck 100 watts.
it has to go some where, if it stays inside, BAM falure.
http://www.pcdied.com/overheated.html
all LT do this, , here is minor packing
see that, if that radiator packs , the war is lost.
http://www.pcdied.com/Filth101/html/image_7.html