Thanks for the tips. I was able to complete 2 of the 5 puzzles. Twice.

Heh, no problem. The trick is completing all of them before the clock runs out. Oh, and you also have to locate the entrance to the mad scientist's secret lair and get in there before time runs out.

Am I just not going long enough?

Correct. If you do it enough, you will reach the end of that screen. I don't know how many times it takes, though. I forget exactly what you get for your troubles. I don't recall if it's required to finish the game or not.