If the mac doesn't have an Ethernet port then you could have bought a
USB to Ethernet cable or Thunderbolt to Ethernet cable depending on
exactly which mac you have.
As you can see $100 to reinstall an OS is a rip off, as it is easy to do it at
home for free.
For future use download a copy of the macOS Sierra installer and create a
bootable USB stick so you can use that to erase and install Sierra without
having to try using the recovery servers or taking it to a repair centre.
Here are the instructions.
Open Safari and click on the link below.
How to get old versions of macOS – Apple Support
Go to Download macOS and click on macOS Sierra 10.12
This downloads InstallOS.dmg to your Downloads folder.
The next section can only be done on a mac that is capable of running Sierra,
a mac that came preinstalled with an OS later than Sierra will refuse to do the next bit.
When downloaded open to get InstallOS.pkg, double-click on
that and an installation window will open, read and follow the prompts,
this does not install Sierra but uses the InstallOS.pkg to create the
Install macOS Sierra.app which you will find in your Applications folder.
(If the installation window asks which disk you want to install to, you must pick
the disk that you are booted to at the time. Not any internal or external disk that
you want to eventually install Sierra on, that is for later.)
The next stage is to make a bootable USB (stick, 8GBs or larger) installer from the Install macOS Sierra.app
in the Applications folder and the createinstallmedia command in Terminal.
There is a problem with making a bootable USB installer with the Install macOS Sierra.app
where it returns an error Volumes/<USBname> is not a valid mount point. There is a workaround.
With Install macOS Sierra.app in your Applications folder open Terminal. (Applications> Utilities)
Copy and Paste in this command
sudo plutil -replace CFBundleShortVersionString -string "12.6.03" /Applications/Install\ macOS\ Sierra.app/Contents/Info.plist
press return
enter your password (your input is not echoed on screen)
press return
Now copy and paste in the createinstallmedia command for Sierra where MyVolume can be replaced with the name of your USB stick
If your USB name has more than one word separated by spaces you would need to type it in as
/The\ USB\ Name
sudo /Applications/Install\ macOS\ Sierra.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume --applicationpath /Applications/Install\ macOS\ Sierra.app
press return
follow the prompts.
This process can take about 30 minutes, Terminal may look like it is not doing anything but be patient.
keep the bootable USB installer in a safe place, so you can access it whenever you feel the need to reinstall Sierra.
Having made the bootable USB installer you're ready to erase and then install a fresh copy of macOS Sierra.
The bootable USB should be plugged directly to your mac.
Restart the mac while pressing and holding the option/ alt key.
In minute or two you will see the Startup Manager, select the USB and press Return.
When booted to the USB you will see a Utilities panel, select Disk Utility and press Return.
In the left hand panel highlight the Disk not the indented Volume, click Erase.
Give the Disk a name.
Format: Mac OS Extended (Journaled)
Scheme: GUID Partition Map
Click Erase.
When Done Quit Disk Utility.
Click on Install OS X press Continue the installation process should start up
follow the prompts.
Just so you know you are not speaking to anyone from Apple here, just users
who are trying to help.
So if you want to use expletives to describe your anger and dismay, don't direct them at me
or anyone else that responded to your questions.