It starts doing the integrity check, but then it finds that the files have been corrupted and will not install the game.
I have re-downloaded the setup.exe about 5 times and each time I have the same problem.
Has anyone else had this problem and does anyone know how to fix it?

I'll redownload it in a second to make sure, but I didn't have the problems when I first downloaded it, I can tell you that.
What do you use to download? If it's the browser it could be that there's still a corrupt entry in your cache. Try a downloadmanager, such as FDM or the GoG downloader. If that's not an option, try downloading through a different browser.
A last thought: Maybe you have too little space on your Windows drive. Many browsers store downloads there while the download is still running, and will go bonkers if there's not enough space.

Some anti-virus products have been reported to interfere with the integrity check. You might try disabling your anti-virus when you first launch the install.

Just redownloaded and reinstalled to make sure. The file on the server is intact.

Spyware products have also been know to cause issues.

I had tried downloading it through two different browsers and I have never had a problem installing other GOG.com games, so I cannot imagine that my anti-virus software is causing a problem.
Anyway, I just downloaded the setup.exe again and it is finally working, so I suppose this thread can be closed/deleted.

Sometimes it happens, that for some reason during the download it can become corrupted. if you have this issue in the future, if using the gog.com downloader or another downloader, try pausing the download half-way through.