I doubt that your router itself has anything to do with it apart. It's more likely that your IP address is, for some reason, been blacklisted.
Start by checking your current IP address:
http://whatismyipaddress.com/
Then disconnect your router from the phone/cable line, wait a minute or so, reconnect it check your IP address again. If your ISP uses dynamic IP addresses, you'll now have a new one.
If your IP address hasn't changed, you'll need to route your internet traffic through a proxy. The easiest way to do that is to use the Tor browser:
https://www.torproject.org/projects/torbrowser.html.en
Once you've got a new IP address you might well be able to access the relevant site(s).