So to follow up, I was able to download and install the game using this link. Once completed, I was able to log into the game. Yay, right? I wanted to make sure that this issue was fixed, so I logged out and attempted to log back in. "Connection error detected. Retrying..." immediately comes back up, preventing me from logging back in.
This is where I'm at now. I've setup Gw2Launcher and set up the patch server to monitor what GW2 is downloading. It looks like its completely dead. No activity at all. Tried to override the DNS setting to force it use port 80, but still no information is popping up.
I don't particularly see this as a problem, as the other PC I tried to log into (successfully, I might add) is running the same anti-virus, configured identically to my PC.
When opening this link to the patch server, I got a return of a string of numbers. I'm assuming this proves the issue something on my PC? I will attempt to launch in safe mode, but I find it so odd that this is only a problem for me after the latest patch.