Installing OSX on a 11 year old iMac

You're welcome.

And I totally understand your situation. My mother is the same way. And though she is well enough off that she doesn't have to be so frugal, her lifelong saving habits are too hard for her to break, God love her! 😃

Meanwhile, I wonder - how did you create your High Sierra bootable USB installer? Since it does not appear to actually boot the computer and install the OS, I suspect there was an error made.

If you're going to press on with this old iMac, if you can coax the iMac to boot into Internet recovery using Option-Command-R you may be offered the latest macOS that is compatible with your Mac - High Sierra.

Otherwise, the best way to reinstall macOS High Sierra will be to properly create and use a bootable installer. The problem with this is since the old iMac appears unable to load any OS, there is no way to use it to create a working bootable installer.

But if you can get your hands on another working Mac model that can run OS 10.13 High Sierra, you can create your bootable installer with that.

These Macs are compatible with High Sierra:

MacBook (Late 2009 or newer)

MacBook Pro (Mid 2010 or newer)

MacBook Air (Late 2010 or newer)

Mac mini (Mid 2010 or newer)

iMac (Late 2009 or newer)

Mac Pro (Mid 2010 or newer)

Note - in all instances above, "or newer" is generally limited to "thru late-2015", as anything newer cannot run HS. Any of these Macs can be used to create a bootable HS installer even if they aren't actually currently running that OS.

The High Sierra OS can be downloaded from the App Store using this link:  

https://apps.apple.com/app/macos-high-sierra/id1246284741

Once you've downloaded the High Sierra OS, you must properly process the downloaded file into a bootable USB installer. Apple’s guidance for that is here: Create a bootable installer for macOS - Apple Support

Good on Matthew for introducing your “elderly” mother to a Mac. Good on her for having a go. Horses for courses as not everyone enjoys the latest trendy M1 Imac.

I am in the twilight of my life and have beautiful 27” IMac (16 years old) natively running High Sierra. Currently running a 27” IMac (10 years old) with Mojave, as smooth as. No problems with the latest up to date browser, the internet or software.

It would good if you could get a bootable external drive with High Sierra (or earlier) (not an installer) which you could either clone to the hard drive or at least test if the internal hard drive is still working.

See if you can find your local apple user group as someone might have such a bootable drive for you to try.

So I encourage you to continue to try and get this ‘old’ IMac to work. I hope you succeed and your mother has fun having a go.

I say this is the kindest way possible (for me 😉)... please don't foist this 14 (!) year old iMac on your elderly mother. You will be doing her no favor by saddling her with a Mac that is obsolete, unsupported in both hardware and software and unable to leverage any of the current secure protocols of the modern internet.

I understand the desire to save money, but the potential for troubles with this old Mac is high, as I suspect you are learning.

Any newer Mac that is no more than 5-6 years old can be used productively for at least another4-6 years, imho.

Don't buy any Mac from an unknown seller. There are too many easy ways to buy a Mac that will be no more than a door stop. Buy direct from Apple or other reputable resellers.

For example: Refurbished Mac Deals - Apple

Or New and Used Macs at macsales.com

Having said that, it does appear that the computer has been wiped, whether properly or improperly is difficult to say without additional sleuthing. But I suspect the failure of the High Sierra installation probably lies in the inability of the installer to contact the recovery server. It's a common problem these days and Apple is not likely to address it.

The good news is there is a workaround for that. Please see Fix #3 in this article for the details: https://mrmacintosh.com/how-to-fix-the-recovery-server-could-not-be-contacted-error-high-sierra-recovery-is-still-online-but-broken/

I couldn't agree more with D.I. Johnson:

... please don't foist this 14 (!) year old iMac on your elderly mother. You will be doing her no favor by saddling her with a Mac that is obsolete, unsupported in both hardware and software and unable to leverage any of the current secure protocols of the modern internet.

It may be unkind of me to put it this way, but it borders on elder abuse. Attempting to use that Mac even for simple and mundane tasks such as email will in nothing but frustration for you both.