I'm sure you've tried most of these https://www.macworld.co.uk/how-to/mac-software/wont-shut-down-3597343/
Right. Been putting this off, but Sky mail (Yahoo) decided to stop support for any Microsoft mail client apart from Office 2019, with 5 days notice (currently using Office 2011). B**tards. So with the computer playing up, no way of getting mail without either going online or installing to Office 2019, I decided yesterday was the day to wipe the thing and start again. What a swine. You can't just update to OS 2.17 Catalina. You Mac has to be running at least OS 2.10 Mountain Lion. The touble is that when I wiped my Mac it installed the 1st OS that it ever came with, 2.8 Snow Leopard. So I spent all day on the bugger. Formatted the HD Reinstalled OS 2.8 Snow leopard. It was so unstable that it kept crashing 2 mins after starting the computer Worked out that it didn't crash in 'Safe Mode' Took ages to create a OS 2.10 Mountain Lion start up USB. Then it wouldn't install, wouldn't reset, just kept rebooting back to the installing Mountain Lion page but got an error message saying I wasn't allowed to install the OS. I was absolutely stuck here for about 4 hours as I couldn't go back to the previous OS. Was just about to book an appointment at the Mac store but tried an internet reset to go back to the 1st OS and start again. Fingers crossed. Then got a message saying "Installing OS Catalina" (Latest version) Decide to go to bed as my nerves and patience are shot. Wake up this morning to a few questions on the final setup. Then Bob's your auntie's live in lover, and it's working. Start re-installing everything. System is stable and the only issue so far is that my new install of Outlook 2019 can't get mails yet, but I'm sure I can sort that. Now just the usual tweaking to do.
Oh yeah. It also now shuts down and the big chunk of 'Other Volumes' has gone now. Time machine is working again so I have backups to reinstall if needed.
Now receiving e-mails in Outlook. Well pleased with this now. 24 hours ago seems a long time in the past.