This is a very important question, as even non-predatory publishers can have problems and face difficult times, eventually closing altogether (e.g. Heart Lung and Vessels).
As stated in the comment by FuzzyLeapfrog, it is very important to double check what you actually agreed upon by submitting your manuscript and when signing the copyright agreement (take notice that sometimes journals do not require you to sign anything but you actually accept their copyright conditions just by submitting your manuscript).
In addition, I would check whether the publisher is still viable, irrespective of the dead website, or not. I would also consider writing to the publisher to inquire on the best course of action.
If the copyright issue is solved, I would definitely consider posting your article in pdf on an open online repository. If no suitable reply has been obtained, you might still upload your article online, in good faith, remaining ready to remove it promptly if requested so by the actual copyright holder. ResearchGate also offers a good means to make selectively available the full texts of your publications.
Conversely, I believe it would no longer be possible to consider publishing it elsewhere in a standard journal (you might tentatively ask a journal of choice if they would be interested, but it is going to be a difficult sell unless your manuscript is really a stellar one...).
As a last resort, you could write a review or perspective on the topic, detailing your prior work with figures and tables (either the actual ones or slightly modified). This will ensure your findings remain always accessible in the mainstream scholarly literature.