Hi chloedaly,
Thanks for visiting Apple Support Communities.
It seems like your iPhone 4 isn't connecting to your home Wi-Fi network. You've tried many good troubleshooting steps, including resetting the router and iPhone, updating iOS, resetting network settings and checking settings.
If you haven't already, make sure that other devices can connect to your Wi-Fi network. Also, try connecting to Wi-Fi networks in other locations using your iPhone. These steps will help isolate the issue to your iPhone or your Wi-Fi network (or internet service provider), and can be found at this link:
If your iPhone, iPad, or iPod touch won’t connect to a Wi-Fi network - Apple Support
If you're connected to a Wi-Fi network but you can’t get online, try to use your Wi-Fi network on other devices. If you can’t get online using your other devices, there might be a service outage. Call your cable company or internet provider for help.
Try connecting to a Wi-Fi network in a different location. If your device can connect, you’ll need to get help with your Wi-Fi network. If it can’t connect to any Wi-Fi networks, contact Apple.
If other Apple devices have trouble connecting to your Wi-Fi network, you may want to take a look at the settings using this article as reference:
iOS and OS X: Recommended settings for Wi-Fi routers and access points - Apple Support
If other devices can connect to your home Wi-Fi network, and your iPhone cannot connect to other networks, try backing up the data on your iPhone and restoring iOS to factory settings using the steps found here:
Use iTunes to restore your iOS device to factory settings - Apple Support
Best Regards,
Jeremy