Wifi says it's connected but we can't use the Internet, what's wrong?

So we have a router/modem that's only a few years old, and it was working fine just a few hours ago. Two iPhone 5S, an iPad, and a Mac, none of them can access the Internet. It says it's connected to wifi on all of them though. We turned off the router and turned it back on, checked all the cords for cat damage; nothing is working. The light labeled Internet on the router is flashing, and the WLAN light is just off. We aren't really tech savvy, so we don't know what else we could try (other than just resetting the router to factory settings, which we want to avoid trying). Any advice from non-tech dummies? Thanks! :)

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