When you say the internet is working, do you mean that you’ve been able to access the specific sites that aren’t working, using another browser? That particular server you give as the example, ping isbn.gov.in, responds to pings, so you could try pinging it in a console. This establishes not only that the DNS is resolving but that you’re able to reach that box (i.e. there isn’t a routing problem in-between.) Sometimes there can be a routing problem on the internet and certain sites or services work but not others, so you need to establish that a specific site is not working only in Firefox but works in another browser, before you can narrow it down to a problem with Firefox.
If you can view a specific website in another browser, and not in Firefox, the first thing I would look at is the proxy settings. Firefox allows the overriding of system proxy settings and establishment of custom settings. Usually, these are profile-specific, however, so if you have created a new profile it would presumably reset this to default to the system settings.
If that failed, I would assume that something might be broken about Firefox and I might uninstall and reinstall it as the next step.