If you're using an Android Emulator and it can't connect to the internet (even the browser won't work), it's likely that it's screwed up picking the wrong Network Adapter from the host system. The Emulator gets DNS setting from a host Network Adapter, so picking the wrong one might leave it with the wrong settings and render it unable to connect.
You now have two ways to fix the issue.
The first one is disabling all the Network Interfaces that aren't connected to the Internet. This is the easiest, but often less viable solution, as you'll likely need to keep those up (for example they might be VM virtual network interfaces, or else).
The second one is specifying a parameter to the Emulator, explicilty setting the DNS. Assuming you want to use Google's public DNS, you'll have to set -dns-server 126.96.36.199 in the run configuration settings.