" a writer's block" feels relatively uncommon to me, so I would probably only use the first one. I suppose you could argue that the first ought to refer to the condition in general and the second to a particular episode of the condition, but in practice "writer's block" with no article is also used for a particular instance.
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Mr. TomWhat's the best remedy for writer's block?Use this. We generally treat writer's block like we treat arthritis. It's uncountable, i.e., it takes no "a(n)".
Mr. TomThanks GPY and CJ!So, can't we consider the "a" in "a writer's block" to be connected with the noun "writer" rather than with the noun "block"? Just like "A child's problems". TomI don't read it that way.