Cannot get any macOS or Linux OS to install on iMac
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.