Error Code: FFXI - 3101

[VoiceMemo]

Alienware laptops are dell so they likely come prepackaged with mcafee antivirus and internet security, i know before you said you checked antivirus but ive seen cases even if you uninstall the antivirus portion of mcafee, the internet security section remains. I would suggest checking this, worst case uninstalling all mcafee from system and retesting connecting to ffxi.

If the traceroute itself went though I'm more convinced than ever it is some software locally that is blocking the connection when the game starts and tries to connect.

Another thing you could do is have someone you trust that has knowledge of computers remote connect into your pc to have a look. Sometimes a fresh set of eyes see's stuff you miss as you maybe too close to the issue and are just missing it.