Maybe we assume that the internet is crucial to be productive (personally), but it might not be necessary. Productivity isn't just about checking tasks.
I mean, how mAny individual creative action require to be online once you chose tools that don't require it?
If by "internet" you meant "fscebook, twitter, Instagram and the like", you already see the problem.
I'd say that delaying gratification somewhat is key. If you stop the internal monkey from getting its immediate hit of dopamine, and get the conscious part of you involved, you can be productive and enjoy it.