It sounds like the DNS server in your WiFi settings is the problem. First, if you turn off WiFi do you get to the site? If so, turn on WiFi, connect and go to settings/WiFi. Tap on the ">" to the right of the network name. Look at the DNS address. It should be the same as your computer, which is likely 192.168.1.1 for most consumer routers. It will usually be the same as the Router address, also.
If it is something first try rebooting your router by removing all power for 30 seconds or so (turning it off is not as certain). This will reset the DHCP server that assigns IP addresses.
If the problem persists go back to the settings for the network as above and tap "Forget this network". The try connecting again (you will have to re-enter the passphrase).
If the problem is still there you can override the DNS setting. Enter a public DNS server like Google's (18.104.22.168) or OpenDNS (22.214.171.124).