This was one of the standout entries of Arnold Schwarzeneger's family comedy phase. It was released in 1996, and generally gets a lot of play during the Christmas season, so it's conceivable that it could have been playing in a supermarket 8 years ago.
The plot of the movie revolves around Ahnold trying to find a particularly popular action figure (based on a kind of Iron Man/Rocketeer character) as a Christmas present for his son (pre-Star Wars Jake Lloyd, fact fans). At the end of the movie, a chain of wacky hijinks leads to him being in a parade dressed up as the character. The suit has a functioning jetpack, controlled by joysticks popping out of wrists, which he activates in an attempt to save his son from a bad guy.
If you ignore some of the funky editing (added by the uploader), the scene in question is on YouTube:
Although it is a full suit, rather than just a jetpack, it hits too many of your points for me to ignore.