1) Can you replace the battery? Look under the heel pad to see if there's a mess of electronics with two coin cell batteries (type probably either 2025 or 2032). Remove said batteries (posssibly with needlenose pliers) and replace them. You can buy replacement batteries at a drugstore.
2) If you've tried putting in new batteries but it stil isn't lighting up it's because the connection is weak. A few things you can try are to remove the batteries then try squeezing the metal battery holder flatter and retry. If that still doesn't work, consider putting something in the recess of the shoe where the battery goes to push it together. I put two pennies underneath each of the battery holders and that was enough to push the connections together when I'm wearing them.
3) See me blog about making your own light up shoes; the ones sold on the market are pretty crappy.