Upgraded El Capitan by mistake - iMac wont boot up

As Phil01234 pointed out there is no 2018 iMac. If it is a 2017 iMac the earliest system it could install is 10.12, Sierra. El Capitan would not install on the 2017 Machine. Therefore, if El Capitan installer did work on your Mom's iMac it had to be a 2015 iMac or earlier.

See if you can Give this a try: boot into Safe Mode according to How to use safe mode on your Mac. It you can then try a normal reboot.

NOTE 1: Safe Mode boot can take up to 3 - 5 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

NOTE 2: if you have a wireless keyboard with rechargeable batteries connect it with its charging cable before booting into Safe Mode. This makes it act as a wired keyboard as will insure a successful boot into Safe Mode.

There is no such thing as a 2018 iMac. Either 2017 or 2019.

A 2017 iMac cannot run 10.11 el Capitan. It came out 2 years after el Capitan (2015), and can only go as far back as 10.12 Sierra. A 2017 or 2019 iMac would not have received an update request for El Capitan.

Given disk utility gets stuck when loading disks, it may be that the hard drive (the mechanical part) has failed.

The fusion drives in those Macs have been known to fail.

At this point, there's very little chance to recover the data of the failed hard drive. You would need to consult with a professional recovery service to get any data out of that hard drive.

Was the iMac not set to backup to an external drive?

You can try connecting an external hard drive to one of the USB ports and see if Disk Utility can recognize it and install macOS on it. Then you can boot from it and see if you can access the internal hard drive.

click here ➜ Use an external storage device as a Mac startup disk - Apple Support

It’s entirely possible the hard drive in it failed.

Make an appointment at the Genius Bar and take it in to have it checked.

FYI: This is EXACTLY why Time Machine exists.