Can't log in after move to new server

I installed Secure Site on a localhost development environment. On localhost, everything worked fine. I had HTTP basic authentication enabled and Force Authentication set to always. With those settings, I was able to log in as user 1, as any user with the "tester" role, and with a guest username.

Then I migrated the site to my live server. I got the login box, but could not log in as any user. Then I went back to the localhost site, disabled and uninstalled Secure Site, and re-uploaded the database to the live environment. I clicked around on live just to be sure that the problem wasn't caused by something silly like not being able to find the database or a missing table or something. Everything worked, so I re-enabled Secure Site. Logged out and got the same problem.

When I re-installed the Secure Site module, it remembered all my old configuration options, even though I had uninstalled the module. Not sure if that means that the module was leaving some setting behind that's causing it not to work on the live environment. The only other possibility I can think of is a server configuration issue, but I'm not sure what to look for. Does anyone have any ideas?