I have no idea what it may be, so let's start with some research, shall we?
How do you connect to internet? Any custom settings? Try resetting them completely.
Check your hosts file for entries for Batoto (%windir%\System32\drivers\etc\hosts or /etc/hosts).
Wipe everything (not necessary, but still useful), open up Chrome, open up Dev tools (F12 or Ctrl+Shift+J), go to Network (make sure it's recording - round button in top left corner of Dev tools is red) and open up any problematic page in Batoto. After loading finishes or fails, right click and hit 'Save as HAR with content'. Now you can zip it (it's plain text) and send it to me (preferably via pm, as it will contain your cookies).
You can view it here or here later on.
Thank you for the help, but apparently after a month of refusing to connect - it suddenly does? I've been 'What?!'-ing like the Doctor for several minutes now. I had checked my hosts file (nothing but commented out lines in there) and turned off my VPN, to record the Network as you had instructed and Batoto loaded to my utter surprise, so I had to make sure that it was off and it was.
Sorry for wasting your time on this issue that sorted itself out somehow. Anyway, thank you both for the help, I'm just going to sit here confused for a few minutes before reading manga.