What's won't my iPhone play videos?

Since yesterday on my mom's Internet, my iPhone 4S hasn't been able to play videos of any kind. Any website that has a video player, it'll attempt to load, then do nothing. I thought it was her Internet, but now my dad's Internet is doing the same. Every page will load on my iPhone, and my laptop that's connected to the same network via Wi-Fi will play videos flawlessly. What exactly is wrong with it and how can I fix it?

Additional information: I have iOS 6.1.3, and I'm highly certain it's an issue with the phone itself. I've been seeing other people on the Internet have this problem but no solutions. Like I said, my laptop on the same network plays videos perfectly. Thus far, I've cleared the history, cookies and cache, backed it up to iCloud, cleared all network settings, and erased all content and settings. Nothing's worked. Pages load instantly, but no video on any website will play and I'm at my wit's end.

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