The last time the Texans made any draft selections on April 28 was in 2012, when that day brought in Ben Jones, Keshawn Martin, Jared Crick, Randy Bullock, and Nick Mondek. The last first-round selection on April 28 was in 2011, when they selected some guy named Justin James Watt. April 28, 2007, resulted in Amobi Okoye and Jacoby Jones.
By my count, that's one all-world superstar of unlimited ability (Watt), a couple guys who showed an occasional moment of competence (Jones, Jones, Crick), a bunch of flotsam, and Tim's favorite teenage cautionary tale.