How are you connected to Internet, if it is through Cellular then in your case it won't work if you have iPad 2 and if you are connected through a Wifi connection then first check if you are able to browse a Website using Safari on your iPad and also once Disconnect from your Wifi connection by going to Settings> Wifi> Select your Network and click on the Arrow on it and then click on Forget this Network and then go back and Reconnect your Network. And then try to Login to Facetime and see if it works and if it still doesn't work then Go through the Steps mentioned in Below link to Fix Facetime issue.
- Ensure that your Wi-Fi network is set up using the recommended settings for Wi-Fi routers and access points.
- If you encounter issues using a Wi-Fi network, use standard Wi-Fi network troubleshooting to resolve interference and other issues.
- If you are using router, firewall, or security software that restricts Internet access, verify that the ports documented in Using FaceTime behind a Firewall are open.
- FaceTime requires a broadband connection. Performance may vary according to network throughput and usage.
Go to Settings>General>Date & Time>Set Automatically>On. Make sure the time zone setting is also correct.
Also try restarting or resetting your iPad and then see if you can connect with FaceTime.
Restart the iPad. Restart the iPad by holding down on the sleep button until the red slider appears and then slide to shut off. To power up hold the sleep button until the Apple logo appears and let go of the button.
Reset the iPad by holding down on the sleep and home buttons at the same time for about 10-15 seconds until the Apple Logo appears - ignore the red slider if it appears on the screen - let go of the buttons. Let the iPad start