My 98 Rodeo started having issues with the starter a couple of weeks ago. When you first turn the ignition it would click once and nothing happened. You could then try again and it would start right away. I was going to check the wiring tomorrow to see if they were loose or corroded. Then today it started fine but when I turned it off the starter kept running and wouldn't stop. By the time I grabbed my tools to disconnect the battery the starter was smoking and so was the positive cable from the battery - it melted the red plastic terminal cover. Anyone else have a smoking starter? What else might need fixin...???

Sounds like the solenoid contacts welded themselves together. Time for a new starter.