did Shakespeare ever get writer's block?

Shakespeare wrote at least 37 plays and maybe more, if scholars are right about his authorships of plays like Edward III and Thomas More.  That's a lot, and I find myself wondering how he would have fared in today's fast-paced publishing world. It used to be that only writers like Stephen King published a novel (or more) a year, but nowadays it seems like everyone from Amanda Hocking to the novelist next door is writing at a blistering pace. that doesn't apply to stageplays of course, unless you're talking about a community playhouse where the players are creating new material for each season, but still. Could Will have kept up?  I suspect the answer is yes. 
True, not every Shakespeare play is a Hamlet (seriously, does anyone ever go see King John except out of curiosity?) but if your other work includes Richard III and Romeo & Juliet, and Othello, you really don't have to write Hamlet every time.