I just tried to access LJ from my computer as a scientific experiment of sorts. Being the scientist that I am, I accidentally typed in "liverjournal." When I finally realized why I got to a page about getting on a transplant waiting list and retyped the URL, I got to LJ and it worked.
OK, a few things that may or may not help:
disconnect the internet, wait like 30 seconds and reconnect.
Reboot.
See if you can get to LJ through a google search for it
Try going to a specific LJ site not just livejournal.com
Try those individually, not all at once
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From the SigmaTo the K!
Polyamorous, Pansexual and Proud of it! It Gets Better