I may be missing something very simple. I did the purchase at the office on the mac and then went home to do my PC tablet. I can click the update in my purchases and it runs. It then says I have no updates?
If this is Mac related please ask in that forum.
It sounds like you're downloading an update script for Logos 3 and the LDLS updater is reporting no updates... Logos 4 installs as a completely different program (rather than upgrading over the top of your existing Logos 3), so you'll need to download and run the installer...
http://downloads.logos.com/LBS4/LDLS4Installer/Logos4Setup.exe