Welcome to the forum, Richard - thanks for trying out Duplicati!
The location of the log files can vary depending on your installation type, but all the usual locations are covered in this post:
When you say it “refuses to launch” do you mean the Tray Icon isn’t showing, the service isn’t starting, or something else?
The second half of this post shows a few ways to see if Duplicati is loaded in Tray Icon or service mode: