Bad connection at the battery is usually what causes it. Often times you'll have corrosion built up between the terminals and not ever know it. Take the terminals off, clean them really good with a wire brush or similar, and you will be good to go. IF that doesn't fix it, you may have corroded battery cables, but I've never seen that happen in a 3rd gen. Not saying it can't. but 99% of the time its just the terminals.
Replacing the belts and having it happen right after is likely just an unfortunate coincidence.