I have been able to fix my client.
Initially, I suspected it was an issue with the hosts file located in the Windows installation folder, but this turned out not to be the case.
I also used a ping traceroute program in order to see where my connection failed, but less than 1% of my pings failed.
I suspected it might have been an issue with my copy of the torrent, and redownloaded the torrent for the second time on my SSD.
Sure enough, after installation, my client was working well again.
It might have to do with faulty sectors of the hard drive I initially downloaded the client on.
I will uninstall and reinstall the game to a separate location to confirm this fix worked.
Thank you staff members for all your help and for all the hard work you've put into this server. This private server is several magnitudes better than official.