Note it's a tower Optiplex --- core 2 duo.

I do not understand this post.

what is the question clearly.

w7 fails to turn off computer,  (this can happen with w7 and super rare w10)

w10 has vastly smarter shutdowns now.

when W7 shuts down it is long process, it asks all apps and driver to shut down, and if any fail( them corrputed)

it can fail. ok?

that is true from w95 to w7 and vista. W8 no comment ,

upgrade to 10 ,  be the last?

your OS is corrupted.

if you booted to Linux demo disk i bet you the PC runs great, and shuts down.

if that was done then in 15minute work you'd now the HDD is  bad and OS corrupted for it.

we test the HDD first, doing full SMART scans, if failed then the HDD IS NO GOOD end story (cause)

if the HDD passes, reload w7, good luck finding that, MS does not sell it nor does DELL.

there is this long drawn out way of tracking shutdowns with old W7 , now 10 years old and officially dead Q1 2020.

the steps are very complex and covered on the MS forum , endless to the extreme.

W10 IMO cured that.

the new W10 , tells you at shut down xyz will hot close, then shows clock  counting down. and then shuts down.

nice.

w7 hangs. are all drivers current on your PC from DELL> off your dell support page??????????

is your MScofig folder empty of junk there. (aka startup folder) if not it can hang easy.

My guess is it's a hardware error but I was hoping someone would be able to be more specific.

FDS