The issue you're reporting is a known issue, our team is currently tracking it:
After defeating the first boss, players that are in a party are unable to interact with the terminal making them unable to progress through �The Eternal Championship: Solo+� Flashpoint.
If the subscription was purchased on Steam, we invite to check on your Steam account. You can find more information on this EA Help page: SW:TOR on Steam.
If it doesn't help you, you can directly contact our support team by phone. Here is our article on how to contact them: How to contact S...Read more
Did you try to follow the instructions of this article (the "What can I do if my Security Key is not working properly?" section): SW:TOR Security Key?
If yes and you still encounter issues, we invite you to directly contact the support team for additional verification. As your issue is about your security key, you should contact them by phone. Here is our article on how to do that: How to con...Read more
The in-game events schedule has been updated for June! This month will feature the All Worlds Ultimate Swoop Rally, Rakghoul Resurgence, and Relics of the Gree events. More details here: SWTOR In-Game Events for June.