URLs don't link to anything

When I add a post, it updates correctly on my homepage, and you can get to old posts through the categories drop down menu on my header bar…but you can’t directly link to them, the URLs don’t work. Even clicking “view post” in the dashboard while I’m editing the post doesn’t link to the right spot!
I haven’t messed with the permalinks – I just have month/name chosen from their 4 options. (I did try switching to the simple default, but that didn’t help, and selecting a shortlink doesn’t get the URL to start working either)
What is wrong??