I just installed on a MSI laptop running Windows 10 Ver. 1803 with a gigabyte internet connection (960mps upload 950mps download). Every time I start up the application, it immediately displays a dialog box stating "Internet access failed" as you can see below. Clicking retry does not help as it simply pops up the same dialog box again, clicking cancel shuts the program down. Clicking ok simply allows the program to run in offline mode which is not what I want.
Quoting from Lego's LDD page:
Sorry. We don’t support LDD version 4.3.10 anymore.
If you still use version 4.3.10 you will experience errors when launching the application.
You can still use “offline” mode if you wish. We urge you to update, use the download link, and install free application for Windows PC & Mac OSX.
There is nothing wrong with your computer, or your internet connection (and it is not just you). LDD will still function normally, albeit in "offline mode."
LDD is now past its end of life, and Lego apparently does not care any longer about collecting usage data on LDD.
The "Internet access failed" message is because LDD can no longer reach a Lego server (188.8.131.52). LDD "phoned home" every time it was started. Now because it can not reach its home server LDD generates this "Internet access failed" message and will only run in offline mode. Apart from spoofing the replies LDD is looking for there is no way to run LDD in online mode any longer.
However, seeing as how Lego shut down the DesignByMe service you are not missing much (if anything) by running LDD in offline mode.