First of all it sounds like you have downloaded an update for macOS High Sierra (10.13.x.)
updates downloaded from the Apple Support Download page can only be applied to a mac
running an earlier version of High Sierra.
What you need to do to install High Sierra on your mac is to download the full installer package
via the App Store. I know you have tried this and it did not work, but believe me it does.
Open Safari, do not use Firefox,
click on this link,
How to upgrade to macOS High Sierra - Apple Support
Go to Section 4 and click Get macOS High Sierra
this will redirect you to the App Store High Sierra page
it should say Get or Download.
If the App Store says ‘Open’ then it is detecting a previous download of the install app
go to the Applications folder locate Install macOS High Sierra.app.
Move it to the Trash, empty the Trash.
Restart, click on the link again, the App Store should say ‘Get' or 'Download'.
Before upgrading make a full back up of your Mac.
Check that third party apps you use have updates available for the new OS.
https://roaringapps.com
Check that your printers/ scanners etc have updated drivers and software available for the new OS.
Connect your mac to your router via cable rather than rely on WiFi.
Do not use your mac while it is downloading
and do not use any other devices that share the same internet connection.
The full installer package is 5.23GBs in size and downloads to your Application
folder as Install macOS High Sierra.app.
Double-clicking on this will start the installation process.
The install app self deletes after installation, so it is wise to keep a copy on
an external disk. You can also make a bootable USB installer for further installs
on any other macs you may want to install High Sierra, it is also useful
if you ever need to reinstall High Sierra and want to avoid downloading it again
or go through the painful lengthy business of downloading and installing through
Apples Recovery Servers.
How to create a bootable installer for macOS – Apple Support