App store Hight Sierra keeps coming up damaged when I try to run OPEN.

When you see 'Open' in the App Store it means the App Store has detected a copy of Install macOS High Sierra.app on your mac.

Open your Applications folder and locate Install macOS High Sierra.app and move it to the Trash, empty the Trash.

Connect your mac to your router via cable rather than rely on WiFi.

Restart your mac, go back to the High Sierra App Store page, it should now say 'Get'

Press that and it should start downloading, do not use the mac while it is downloading

and do not use any other devices that share the same internet connection while your

mac is downloading.

Naw, not damaged, it's just that you have an old copy already in Applications, there are 2 cures...

Disconnect from the Internet & set the Date back to 2014, then you can run the Install MacsOS High Sierra App in Applications, so expired Certificates are not expired.

Or... trash the Install MacsOS High Sierra.app in Applications then a new copy can be downloaded.