Problems on initial admin login

I am trying to install the newest version of WP and am having problems initially logging into the admin account so I can set up another user and start getting my blog set up.

Specifically, when I go to log in using the admin username and the password that was generated, it appears to just refresh the same page. No error message, no visible signs of problem, except it doesn’t take me to the admin section, it just shows the same login screen.
I have tried resetting my password using the built-in feature (I get an invalid key error, and yes, I’m copying and pasting the whole address).
I have tried getting into my MySQL setup and changing the password for the admin user through that (using an md5 hash generator to “convert” the password).
I have tried disabling all of my firefox add-ons and tried logging in using IE, Opera, and Safari.
I have also tried uninstalling and reinstalling WP on my account (three times so far), and every time it appears to install just fine, but won’t let me log in.
I have WP running on another server, and have no problems logging into that installation.
Any thoughts as to what might be going on or what I can do to get this working?
Thanks in advance for your help.