A few days ago after zoning from Omega Leonis to Eta Eridani with my Klingon captain, the game stopped responding and eventaully dropped me whilst on the loading screen, since then every time I've tried to play my Klingon captain it gets to the end of the loading screen and after 20-30seconds eventaully disconnects me. Occasionally it loads, but the game doesn't respond, I can't move or anything.
Today the same happened with my Federator captain when zoning from Sirus Sector to Eta Eridani.
I've reinstalled the latest graphics drivers, reinstalled STO and re-verifed all the files with no luck.
Your nettest results look great, so network connectivity doesn't seem to be the problem. Have you checked the system for overheating or faulty components? Checked your even log for application crashes?