Ok. I just re-installed EVE: Online, but then I pressed "play" and Steam stopped responding and shut down. I restarted, did same thing, happened again. And again, 2 more times. halp please 
EDIT
Now, it's saying "Failed to contact key server" when I press play... wutAfter about 30 minutes of my struggle, for some reason, it just worked. It must be because of RND being such good luck for me.