If you boot up an Apple II without a disk in the drive (or something incredibly simple like that), it drops into AppleSoft Basic. That's how I learned that one could program a computer. For sample code I could turn to a number of magazines about my computer, or the manual that came with it. No questions or outside research dependent on anyone else (including the Internet) were required. This was when I was of single-digit age. The barrier to entry was tiny (type "10 print hello world" at the command prompt). Nothing like that exists for a curious child at this point unless their parents take the initiative, or the child waits until they're older.
I was a little after this, but it was similar. Dad had QBASIC on his Gateway2000 machine that we played Oregon Trail, WITWICSD, Prince of Persia and so forth on. I had fun with qmaze, qbricks, and so forth - and then I asked dad if there was a way to cheat. He showed me the qbasic ide, and handed me a qbasic manual. And then he said, "Have fun!" - I was in the single digits when this happened, as well. Unfortunately, I never really made much with it - just had fun making custom brick shapes in the tetris clone.
I was lucky, and in middle school, we had an elective that allowed us to use lego robotics and logo to do some really basic stuff (one of the projects, if I recall, was building a robot arm to sort bricks based on color). Not much problem solving involved in it, though - they just gave us "type this in" and "put the legos together this way" instruction booklets. If we had been encouraged to solve the problems for ourselves, I might have gotten a lot more out of it. As it is, I don't recall any logo at all.
Didn't do any more programming until sophomore year of high school, and things like optimized sort algorithms really caught my imagination. Haven't really looked back since...
