I think my phone is broken but I am not sure. I have always been able to access my home internet and I still can. I can run small apps, like Clash Of Clans, but I cannot run any larger apps. I cannot use the App Store (It says I need to connect to wifi to access it even though I am) I cannot use Discord and many other things. And I really do not know why. Like I said, I can use apps that require little data usage but nothing large. It is definitely connected. Even if I switch to my mobile data I still have this problem. Please help.
Try enabling your airplane mode for 10 seconds. Then disable and try accessing your App Store/apps. If this does not fix it. Do a hard reset.
Hold close iPhone button/sleep and the home button, till the screen blacks. Wait a few seconds and then hold the close iPhone/sleep button to turn it back on. (iPhone 4's top button)
If you don't trust the hard reset idea, google it.
Hope this helps. :)