Now that you’ve mentioned it’s Aljazeera I’m almost certain it’s your government or ISP that’s blocking it. Lots of countries where censorship is law block Aljazeera.
You’ll probably need to use your VPN to access it, plain and simple. If they’re really only using DNS to block the site then you may be able to access it by just using a different DNS or using direct IPs, but I doubt that’s all they’ve done.