A TALE OF TWO COMPUTERS

I am logged in on my (much better) computer in my office at work but when I go home and try to log in, I can't even get to the Log In site...when I click on "Log In"...it takes me to my home site, but I can't access anything because I'm not logged in...and it tells me to log in first, but I can't....so I have no link to the "Log In" site. Yet on my computer at work I'm logged in and since I never turn this computer off, I just stay logged in...I'm afraid to log out because I might not be able to get back on...what do you think the problem at home is?