Cannot get any macOS or Linux OS to install on iMac

I am having a strange issue with my Mid 2010 27 inch iMac - I get the chime, I can get into recovery partitions and into installer USBs no problem...but I can't seem to get a single install working. It'll just reboot a minute or two into installation. I can get into the desktop of an old Lion drive - but I get the "your computer needs to restart" error. It also failed halfway through internet recovery CommandR

I've already tried SMC and NVRAM resets of course.

Here is a picture of the kernel error I am getting. Any help with this would be appreciated.

Original image: https://imgur.com/maSoJIE

Edit: attempt to make the original more legible [not hugely successful]

Solution 1:

Firstly: check the disk.

A ten-year-old Mac is a likely candidate for a failed hard drive. Use Disk Utility to check the drive.

Secondly: check the rest of the hardware.

If you have a bootable system on an external USB drive, which you know boots on another Mac, see if that will work. If it doesn't, then the problem is likely a hardware fault.