LOL I own a 02 Sport trac also, when I got it from th eprevious owner, he said the 4x4 does not engage.... the hi 4x4 does but not the low range.
I put the truck in N and hit the button, it works perfectly.
So when you say the 4x4 does not engage, what are the conditions and what happens when you hit the 4x4 hi button?