Wi-Fi access on computer but not iphone

So i just changed my internet router from verizon because the old one was working very slowly. The new router works fine on the computer and my laptop, but it doesn't work on my iphone 4s. It says i have all four bars, but when i use internet, it never loads and in a few minutes, it says that safari can't connect to site because there's no internet connection.
what is this and what should i do to fix this? Please help!

Added (1). I've tried restarting my phone and even reset my network settings.resetting my network settings worked for about… 15 minutes and after that it comes back to what it was before. Is it just my phone?

Just turn off and back on your iphone. This should fix the issue.