I'm having a similar issue in that I can load the splash screen, but when it wants to ask for a login it just freezes.
I don't know if it has something to do with my anti-virus because before the "CryDev Login..." shows up AVG asks me if I would like to move files pertaining to CryEngine into my vault. When I hit ignore it just freezes like above.
I've tried restarting, as well as turning AVG "off" and nothing I can find seems to be working.
EDIT: Turns out I was far too excited to get my hands on CryEngine and didn't even read the AVG message. It's working properly now.