When I just my one laptop, through chrome, to visit a specific education website (www.ccbcmd.edu) I frequently encounter a dns lookup failure and the page shows a rough sketch of what is likely a t rex. Anyway, when I use my mac this does not happen, so it should be some local setting on the laptop that is causing this. Any ideas?
You are probably using chrome, unless some other browser is using that error display.
DNS info may be cached on your local machine, which can lead to connection problems if the cache is wrong. Chrome allows control of the local cache through the browser:
Oh, I didn’t notice that you SAID you were using chrome. Well, I could have deduced it anyway …
It’s a Chrome feature (game actually):
Because Apple has no humor. 
I have gotten this but it doesn’t explicitly say it’s a DNS error. What is the error message you see? I see T. Rex if I have no Internet connection, or if an attempt to reach the server times out.