If FeedDemon says it's unable to connect to the Internet or it's unable to make a secure connection to Google Reader, then chances are your firewall is blocking it. This happens most frequently after upgrading to a new version of FeedDemon - your firewall may have permitted the previous version to connect, but it doesn't recognize the new version and blocks it without telling you.
This can be resolved by removing FeedDemon from your firewall's list of approved applications. The next time you run FeedDemon, the firewall should ask you whether to allow it to connect.
If you're not sure how to do this, stop by our support group and let us know which firewall software you're using (popular choices include Windows Firewall, Norton Internet Security, ZoneAlarm and McAfee Personal Firewall) and we'll do our best to step you through it.