Yup, same thing here -- I've been occasionally clicking on the purchase button to see if the problem had been fixed (and, most of the time, no, it had not been) but, then, out of nowhere, the upgrade window suddenly started working. I was able to add license and am now back up and running.
Like Peter, I'm also darn certain that there were no changes, at my end, that would have caused it start working and am assuming that CocoaTech finally fixed something at their end.
My Purchase window was initially blank, but then did populate. However, I now have a "Free Trial - Buy Now!" on my desktop! I've already bought the upgrade and activated the license. I'm on Mojave 10.14.6 (18G1012).
I just tried to try (!) Path Finder 9, freshly downloaded. I'm coming from Path Finder 7, which I'm still running stably on 10.13.6. On launch, PF9 greets me with an oversized "Purchase" window that briefly shows (nothing but) a Path Finder logo that quickly moves to the bottom and off the screen. The window is then blank. I cannot close it, it wiggles wildly when I drag it across the screen, and no other Path Finder function works (except quitting via the Dock icon).
I though this might be an artifact from my PF7 installation, so I trashed everything Path Finder via AppCleaner and retried. Same show. I cannot even start up the application.
I've always loved Path Finder and considered it essential software, so even after having a similar experience with PF8 and watching issue after issue pile up here, I thought I'd give version 9 another try. But seriously, this is simply ridiculous. Two major new versions and the app won't even launch!
If you want my money, make this f'ing thing work again before introducing "new features" and switching to shorter upgrade cycles that would cost me money every year. Up until PF7, this was a serious, highly capable and largely very stable workhorse program. Since PF8, it is little more than a clown show. I'll be staying on PF7, and when that stops working due to macOS updates, unless the "new" Path Finder is fundamentally improved by then, I'll be a lost customer.