Here's my money quote:
Today's ceremony, however, has very special meaning. Because today we are not merely transferring power from one administration to another, or from one party to another -- but we are transferring power from Washington, D.C. and giving it back to you, the American People.
I heard it timed at twenty minutes, then later someone said it was only sixteen.
You're right to point out that he said "I" only three times. He said "we" however, 45 times.
I find this particularly significant because commentator Mara Liasson, on NPR before the speech, suggested that we listen for this detail because Trump was all about "I" during the campaign. She probably heard me yelling at her through the radio, "Did you ever notice how much the sitting president talks about himself? The Narcissist in Chief?"