Try running a TraceRt. I have been on and off the website consistently for the last 3 hours and haven't experienced any issues.
Edit: Just bought a Key on the website C-Store and it only took me a few seconds. Now I need to log into the game and put it on the Exchange.
STO is about my Liberated Borg Federation Captain with his Breen 1st Officer, Jem'Hadar Tactical Officer, Liberated Borg Engineering Officer, Android Ops Officer, Photonic Science Officer, Gorn Science Officer, and Reman Medical Officer jumping into their Jem'Hadar Carrier and flying off to do missions for the new Romulan Empire. But for some players allowing a T5 Connie to be used breaks the canon in the game.