Unable to reinstall High Sierra on 2010 iMac via USB or through internet recovery

Creating a bootable USB with Transmac on a PC never works.

Borrow a mac to make the bootable USB.

The problem with restoring the mac from Apples Recovery Servers might be down to

Apple still using versions of their software with expired certificates.

Try this workaround, we are going to set the time and date on your mac to a date previous to the expiry date of the certificates.

Connect your mac to your router via cable, not WiFi

Boot to your Recovery HD, click on Utilities in the menubar select Terminal.

Make sure WiFi is switched off, it can reset the date back to today.

Enter a new date, for example or just copy and paste

sudo date -u 011421002017

press Return

enter your password

press Return

If Terminal returns an error saying sudo : command not found, then try again without sudo.

just enter 

date -u 011421002017

press Return

You won't be prompted for a Password if you did not need to use sudo

Once the date has changed you can quit Terminal.

Now try downloading the OS.

Click on Install OS X, press Continue.

If this works then when the OS is installed and booted up you can Open System Preferences> Date & Time

and reset the time back to today.

It seems that your Mac has a recovery partition for High Sierra, so this is what I would do:

• Plug the Mac into your router with an Ethernet cable. Don't rely on wi-fi to get this job done.

• Plug in a USB wired keyboard.

• Restart the Mac, and when you hear the startup chime, press and hold Command-R until you see the Apple logo and progress bar. This should get you booted to the Recovery partition (10.13.6).

• From the Mac OS Utilities window, click Disk Utilities. In **, click View > Show All Devices. Select the topmost internal device (probably named Apple HDxxxxxxx). Click Erase and then name the drive "Macintosh HD", select Mac OS Extended (Journaled) as the format and GUID as the partition map scheme. Then click Erase to wipe and repartition that startup drive. Once ** reports the task complete, quit ** and then select "Reinstall Mac OS" from the Mac OS Utilities window.

With any luck you should now be able to reinstall the OS from the recovery partition. If the Mac need to reach out to the net for resources, the ethernet connection should be more robust than a wi-fi connection and get you through this.

How to reinstall macOS - Apple Support:

click> https://support.apple.com/en-us/HT204904

Are you holding Option key at startup to see if USB is an option?

Actually the DMG even if restored needs OSX to boot first, if you can get into Terminal using CMD+r keys see if you can do this with the DMG...

How to create a bootable installer for macOS

You can use an external drive or secondary volume as a startup disk from which to install the Mac operating system.

These advanced steps are primarily for system administrators and others who are familiar with the command line. You don't need a bootable installer to upgrade macOS or reinstall macOS, but it can be useful when you want to install on multiple computers without downloading the installer each time.

What you need to create a bootable installer

• A USB flash drive or other secondary volume formatted as Mac OS Extended, with at least 14GB of available storage
• A downloaded installer for macOS Big Sur, Catalina, Mojave, High Sierra, or El Capitan

Download macOS

• Download: macOS Big Sur, macOS Catalina, macOS Mojave, or macOS High Sierra 
• These download to your Applications folder as an app named Install macOS [version name]. If the installer opens after downloading, quit it without continuing installation. To get the correct installer, download from a Mac that is using macOS Sierra 10.12.5 or later, or El Capitan 10.11.6. Enterprise administrators, please download from Apple, not a locally hosted software-update server. 
• Download: OS X El Capitan
• This downloads as a disk image named InstallMacOSX.dmg. On a Mac that is compatible with El Capitan, open the disk image and run the installer within, named InstallMacOSX.pkg. It installs an app named Install OS X El Capitan into your Applications folder. You will create the bootable installer from this app, not from the disk image or .pkg installer.

Use the 'createinstallmedia' command in Terminal

1. Connect the USB flash drive or other volume that you're using for the bootable installer. 
2. Open Terminal, which is in the Utilities folder of your Applications folder.
3. Type or paste one of the following commands in Terminal. These assume that the installer is in your Applications folder, and MyVolume is the name of the USB flash drive or other volume you're using. If it has a different name, replace MyVolume in these commands with the name of your volume.

High Sierra:*

sudo /Applications/Install\ macOS\ High\ Sierra.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume

Do you see a "BaseSystem.dmg" file located anywhere on the USB stick TransMac made or within the macOS installer app that was downloaded by TransMac? If so, then you can either "Restore" this "BaseSystem.dmg" file to the USB stick or you can use Linux to convert the .dmg to a standard non-compressed raw image file where you can use Etcher to "burn" the image to a USB stick. This will create a bootable macOS recovery mode like USB stick which acts like booting into Internet Recovery Mode.

Have you tried booting into Internet Recovery Mode using Command + Option + R to boot into the online macOS 10.13 installer?

It is highly unusual to have more than one memory module fail especially a Crucial or Apple memory modules. Macs are very picky about the memory they use so you always want to order the exact part numbers suggested by one of the tools on the Crucial website. Usually when you purchase memory for a Mac from Crucial the packaging of the memory will be labeled "For Mac". If you order the incorrect memory (even if the technical specifications appear identical) you may get intermittent issues even though the memory is Crucial branded.

If you have the correct Mac compatible Crucial memory and it has failed, then Crucial has a lifetime warranty on their memory as long as the memory is still being made (or is still in stock). I'm not sure how Crucial handles incompatible memory issues 18 months later (if it was determined the memory was not actually for a Mac).

Thanks, for following up to let us know the memory was the problem.