Wasn't a DIY jet-powered something the co-star of a Darwin Award several years ago? I guess if you want to take the lead in a sequel, Seth Kettleman from TransTurbine in Maryland has the vehicle for you. The Boeing Boss is a go kart powered by a custom-configured Boeing 502-12 gas turbine engine. Kettleman calls it a "land-jet," which I'm pretty sure is synonymous with "Hope you don't live too far from a hospital."
In action, the Boss produces over 300 pounds of thrust. I can relate.