The Dropbox app won't install on my new desktop (the installation window disappears).

Hey foweyman, sorry to hear about that. 

What do you see exactly when the installation fails? Can you send over a screenshot perhaps?

Let me know when you’re ready.

No error message.  The installation pop-up window just disappears after 20-30 seconds.

I see. Can you also give our offline installer a try and let me know how that goes?

Other than that, do you have any antivirus/firewall programs running that could be interfering with Dropbox? If you do, I’d like you to disable them temporarily, restart your computer and try to install the Dropbox app again.

Same result with the offline installer.
Only the Windows built-in antivirus. 

Hey foweyman, what's your computer's exact Windows version?

I'm assuming you have already restarted the computer, but if you haven't, can you please try to see if it helps at all?