FWIW, my nephew -- with whom I share a router & who has the same video card -- is playing right now. Neither my brother nor my nephew have had any trouble accessing the servers; only me.
It's very frustrating, especially since I was playing just fine yesterday, before the servers went down at 1:30 PST. I was able to log-in for a half hour at 5:00 PST, but then I had to log back out to make dinner & feed my cats. I haven't been able to even get to the log-in screen since.
Is this a common problem? Just a server capacity issue or something?