Many Steam users have recently encountered "No internet connection" error message when downloading or updating a game.
This error message occurs due to a problem with the Steam servers and not with your internet connection as indicated. There is no solution to fix it and you will have to wait until the servers are available again.
If you encounter this error, remember to check the status of the servers by going to the page dedicated to Steam on the Downdetector site.
If a problem affects the service, you will quickly see reports on this page which form a graph allowing you to see if several people are having problems with Steam. Finally, if you still can't download after waiting a while, you can contact Steam support for help.