Thanks for the additional details. The Daily Neopets' security certificate is fine and is in functioning order.
What appears to be happening is that thedailyneopets.com is being blocked by OpenDNS, a DNS provider you're using to access the entire internet. We need OpenDNS to unblock thedailyneopets.com or use a different DNS provider. Two steps here to help TDN get unblocked:
Submit a message (with these screenshots from here) to
[email protected], requesting that the domain thedailyneopets.com be unblocked and is a legitimate website
In the mean time, do not use OpenDNS to access the internet. Consider using an alternative like Google DNS (8.8.8.8 and 8.8.4.4). To switch your DNS provider from your connection, follow this for MacOS or Windows.
Let me know if switching your DNS provider worked for you.