Mary,
In 2 Tim 3:16, isn't the Greek for 'inspired' theopneustos, literally 'god breathed'? It appears the writer was intending to convey the idea that the Scriptures were 'influenced or guided by divine or supernatural inspiration' (the first of your definitions).
Of course, that doesn't mean the Scriptures really were inspired by god, merely that the writer claimed they were! Also, when he wrote of "All Scripture," he would be referring to what we now call the Old Testament ('Hebrew Scriptures' in Watchtower-speak!).
So, is there any evidence the Old Testament was inspired by god? Not if you believe the evidence in "Who Wrote the Bible?" by Richard E. Friedman, which clearly illustrates from the Old Testament where original texts were 'cut and pasted' to suit the, usually political, aims of the original authors.
No divine inspiration there, then, and obviously none in the book of 2 Timothy!