Login Loop

I got a newly set up WordPress blog and it works fine, from home. I can log in, add post, whatever.
However, I tried loging in remotely and the login screen just loops back. In otherwords, at the login screen I enter my username and password, click OK and the page merely refreshes. No errors, nothing.
Also, when I logout at home, it doesn’t seem to really logout – just refreshes the admin screen. I suspect that the two behaviors are related.
I’ve looked around the forums and have found answers to passwords not being accepted, but not my particular problem. Any ideas?