After reading all these posts, this sounds like a routing issue to me... It's not happening to me or I'd try this myself.

If someone is experiencing this and has a little tech background, what I'd like to know:
If you can get your stuck character moving again by logging in on a friend's PC, use Wireshark or some similar packet tracking program to find out the IP address of the server you're talking to.
Take that IP address back home and try to ping it and trace it.

It may not be a problem with either your ISP or SE's servers. It's likely somewhere in-between.