So far I've done the time sync, checked all updates which are all current, double and triple checked my router/modem all connections to make sure they are seated, added exceptions in the firewall, disabled the firewall as well as multiple restarts. Still no luck for me so far on this end.
I will say I've only experienced this on my windows XP box and not my win7 box. I'm starting to think this is mostly just xp related.
Also for those wondering what the time sync has to do with anything, it's the SSL certificates that your computer gets from Riot servers during the login authentication. It might not make sense, but its incredibly important.
I just tried pinging the login server off two different computers in my network, xp sp3 and win7ult and neither of them are able to ping the login server via ip address or url.