Website domain name does not opens and IP address opens

Website domain name does not opens and IP address opens

I have a problem to access to a website I am working for. When I type in
their website domain the web browser shows "This webpage is not
available". I also try to ping domain name from command prompt and same
problem.
However when I type in website IP address, it works without any problems,
I also successfully ping it.
I also noticed that when I use proxy with different IP address then my
default one I can access website on both, domain and IP. I tried so many
things and none of them works so I am without options.
Any suggestions are most welcome. Thanks!