Every single time I've had login issues with GFWL its been because its not happy with the state of the TCP/IP stack on my PCs. For some reason it gives crap logging in if the stack isn't in an almost default state.

You can try this to reset your TCP/IP stack:

Run (WindowsBtn + R) -> cmd

Code:
netsh int ip reset resetlog.txt
This will reset any settings you have for your network adapter as well (static IP address/DNS etc.), if you use DHCP then don't worry about it.

+1 for GFWL being garbage. I really don't get why any games developer uses it since it has been unanimously hated by PC gamers everywhere since its inception.