can not seem to reinstall os x el capitan to erased hard drive

If you reboot while holding down the option/alt - command - R keys, that will boot you into Internet Recovery, and install the newest OS that is compatible with your computer. The boot into Internet Recovery is very slow.

Boot from Recovery. Regular or Internet, depending on the specific Mac mini. Follow the directions to wipe and format as GPT and re-install.

Or use another local Mac to build a bootable installer, and follow the directions there to boot and use that. You'll want to download El Capitan (10.11)—but that may not be in your previous purchases—or High Sierra (10.13), or Mojave (10.14).

I wouldn't bother with something as far back as El Capitan, unless that's the newest OS X supported by this Mac mini.

How to know which model? Flip the Mac mini over and check the model number on the bottom. Or post that.

Or fetch the MacTracker app from either the Mac or iOS App Stores, and look up the model number yourself. (There can sometimes be a couple of related Macs sharing the same model number, but it'll get you in the right range then.)

Or fetch the serial number off the bottom of the Mac, and enter that into the Apple warranty coverage site. Don't post the serial number here, though.

Boot from Recovery. I'm guessing that the Utilities pop-up that you're seeing is the installer. See the Recovery discussion for details. Wipe. Reinstall. See my reply for additional details, and for the alternative approach of building and using a bootable USB installer.

_light_guy_ wrote:

Reading through the how-to-create-boot-installer has me concerned as it prompts for an admin password.

As I said above, this device is second hand...

Or use another local Mac... The admin password required here is that of another Mac. The second Mac is the one that builds the installer. Your internal storage is already erased, so you don't have that Mac available to perform this sequence. Then transfer this to the problem Mac, and boot and use it per the information in that Apple build-bootable-media article.

You are welcome. What options do you see on the Utilities Menu? Is Disk Utility an option? An install option?

Reboot while holding down the option/alt - command - R keys and when you see the menu, if you have erased the disk as you posted earlier, click the Reinstall OS X option.