@fifthhouse
I once struggled for a whole day with the same problem..
It occurred on just ONE of my installations (form MANY), on a specific server .
It was 1&1 hosting server from germany (not reccomanded BTW).
In my case, the redirection rules were changed by a plugin (adminimize) and More-Fields (at least I think) so :
1. you need to try and deactivate plugins from the DB
2. Reload all WP files again, after DELETING the old ones (not overwrite) - remember to NOT delete config.php .
3. you should try to look at your .httaccess files (possiably also post here) , create one if there is none on your server at the root and see redirection roles there.
4. if none help, reset your user or create a new admin user from DB - while this option is not reccomanded, i could guide you how to (I hope) if everything else fails .