What if you do ping hostname on Windows command-line (cmd.exe)?

I am doing a project for a Database class in school. Our database is hosted on the school's server and I can connect to it fine at school, but get the "Host does not exist" error when trying to connect at home.

Per the "Host does not exist" help page, I have made sure my firewall is not blocking it and forced IPv4. Because it works at school, I think I can safely assume it's not because I'm mistyping or a problem with the domain name being too new. I would also think it wouldn't be a problem with the DNS server as I have tried multiple times over several days and I haven't wrote any scripts yet so I don't think it can be that either.

In a situation like this, what do you recommend doing? Thank you for any help.