For reference (and other users planning on moving their Showkase sites), the 'Changing Your Installation Directory' instructions can be found here.
The first thing I'd do is make a complete backup of your Showkase site in case anything goes wrong and you need to reinstate the original files at a later date (to try something different).
Have you been able to run the setup procedure after moving your Showkase site? (Normally, after moving a Showkase site, Showkase will detect that its path has changed and automatically display the setup page to update it.)
If so, did it seems to go smoothly or did you encounter any errors along the way?
Being that the error message you have encountered refers to the password for your Showkase site, please try the password reset procedure to see if this helps.
FAQ: I lost my password, how can I reset it?
It might also help to run Showkase in debug mode to see if a more detailed error message is displayed in the application's status bar which might help to pinpoint the cause of the problem.
Open your 'showkase/admin/settings/constants.php' file in a plain text editor and change line 12 from:
If this provides more detailed information about the problem, please let me know.
I hope that this helps (or at least points you in the right direction).
Please let me know how you get on.