AVR Freaks

And Disney has their "World of Color" hats. Which are a complete PITA to carry around the park with you all day before attending the show; I like the wrist-band idea much better.

Somewhere in between grueling sales-jobs and manufacturing nightmare, there is some enviably fun design work that goes into these things...

Not an expert in this, but I'll throw out a couple possibilities that come to mind.

Option one: You might have given it a static shock when removing or reinserting the batteries, in which case some part of the electronics would have been damaged. This is pretty easy to do without even knowing about it.

Option two: the wristbands might store their status (such as whether they're in impact mode) in volatile memory, so removing the battery effectively resets them to right out of the box - if it didn't light up on movement when you first got it this is probably be the case. Some of the info on the company's website would seem to imply that it is not, however.

Unfortunately, if it is the case that would mean that the only way to turn it back on would be to send the IR impact command that they sent at the concert to put it into that mode, which you don't know. With enough experimenting with an IR transmitter you might stumble onto it, but the possibilities are vast and I'm guessing you don't have one of those around the house anyway if you're "a non-techie," so the short answer is it could be just about impossible to re-trigger it.

Since this is your first post here (Welcome!) I'm guessing you're here looking for a solution rather than as an electronic hobbyist, but making something like this wouldn't be entirely out-of-reach as a beginning project.