When you're having network issues and can't access the Internet, isolating the problem isn't always easy. As Ghacks points out, many computer systems have networking tools available to help you figure out the issue. Tools like ping, traceroute, nslookup, and netstat, are all proven utilities that help identify network problems.
If you're not familiar with using those tools or would like a simpler all-purpose tool, Google has created a Chrome app called Chrome Connectivity Diagnostics. It contains several different networking tests with the results displayed in an easy-to-read format.