Won't boot & won't recover

One of the house iMacs is a mid 2011 21" running High Sierra 10.13.6. All of a sudden it apparently it started to reboot itself. And hung. She Who Must Be Obeyed (her machine) had no idea what happened or when. I have tried all the standard recovery options, including a bootable installer on a thumb drive, and nothing works. The best I can do is get to a screen with a dropdown to pick a network, and all that is there is an X. The regular HD partition shows along with the HS recovery partition. Whether I select the regular HD or the recovery partition the process indicator gets stuck about 75% of the way, and just stays. I did notice the machine is extremely hot. I can feel a slight stream of air out of the top slot, however that part of the case is almost too hot to hold my hand on. I've powered down and will try again after a few hours. And I will vacuum the slots, just in case. I also checked her TM sparse bundle from my iMac and the last backup was 6/29 (mine is current so I believe TM is backing up), so there will be trouble if this old iMac is DOA.

Other than prayer is there anything else to try?

If the old iMac is shot, it is possible to remove the HD and put into a housing, and recover the data?