Could my firewall or antivirus software be blocking Call of Duty's connection?

Yes, it's possible. Your firewall or antivirus might be incorrectly identifying Call of Duty as a threat and blocking its access to the internet. Temporarily disable your firewall/antivirus (at your own risk) to see if that resolves the issue. If it does, add Call of Duty's executable files to your firewall/antivirus exceptions list.