Hey @Idelone, thanks for your report.
It's true that Dropbox no longer supports Windows 7. The minimum requirement is now Windows 8 or higher. That said, your results when trying to install the desktop app may vary, exactly as you noticed.
I know it's not much, but I hope this helps to some extent, Ian.
As for you now @hlussiatti, could you try a clean, advanced reinstall and let us know how it goes?
Just make sure to toggle off the early releases from your account's online settings to avoid reinstalling a beta version and download and install the desktop app from this page directly.