It's got to be almost impossible to determine whether or not he coined any of the words which are first attested in Shakespeare. They could have been slang terms, colloquialisms, or words found only in rare or lost manuscripts. If you look at the amount of writings put out during that period, a large chunk of it has to have been by Shakespeare. Words that were public knowledge at the time but hadn't found their way into a book or play would be considered today to have been coined by Shakespeare.
Seanahan and neveau have between them said just what I was thimking. Any number quoted must be an estimate because in truth there is no way to know if Shakespeare coined a particular word or simply used one that has no earlier survivong citation which may have been in use nevertheless. Given that he was writing the Eastenders of his day (popular entertainment for the masses) he was likely to use the kind of language they would know and appreciate. I'm very dubious of any figure as exact as 2035. And 6000 does seem high for "made up" words - which is what new coinages are - unless there was a running joke among the theatre going public along the lines of "Let's go see WIll's new play tonight, I love the way he makes up all those words. He's a real commedian."
"No man but a blockhead ever wrote except for money." Samuel Johnson.