Argh! I am getting the dreaded 500 internal server error.
I have tried installing the latest version 1.4.10, and installing the three folders index.php, /themes, and /zp-core as suggested by the instructions here.

Here is what I get: (the url line /zenphoto)
returns this (in the url line) : http://mysite.com/zenphoto/zp-core/setup/index.php?autorun=gallery
Then on a white page:
The server encountered an internal error or misconfiguration and was unable to complete your request.
Please contact the server administrator, and inform them of the time the error occurred, and anything you might have done that may have caused the error.
More information about this error may be available in the server error log

I did contact my server admins, they were able to fix the same issue with Gallery 3 (THAT works now), but still having problems with zenphoto. I was able to generate a phpinfo.txt, I need some help. I have looked at other discussions vis a vis the 500 error and can't find my solution yet.
TC

Apparently Zenphoto cannot find .../zenphoto/zp-core/setup/index.php.
Please check the zp-core folder to see if the setup file and folder are present.
You should have one setup.php file and a folder called setup with 10 files in it.

OK we are up again! Altho I am getting the following screen occasionally at the top of my admin pages:

Zenphoto has detected a change in your installation.

Your database software has changed from MySQLi 5.5.32 to MySQLi 5.5.44.

The change detected may not be critical but you should run setup at your earliest convenience.

I am happy I am up. What will setup do that is so important? I do NOT want to lose zenphoto again!

Apparently I am running 1.4.5.9
I thought I was upgrading? I can't imagine what happened, but I am NOT running 1.4.10. Should I attempt to redo setup, and should I attempt to install the 1.4.10 version?

The message you get is because...well, the software on the server has been updated by your host. Zenphoto detects that and advises to run setup again. See it as a precaution. Zenphoto will notify you if there are incompatibilites with the updated server software. Fortunately this rarely happens.

Yes, try to upgrade again.
Backup your database and possible modified themes.
Upload the necessary files/folders for 1.4.10 as you did before.(best is to remove the old ones first because overwriting sometimes goes wrong)
Run setup.

Note that if you DO use a modified theme you'll definitely have to update it manually because some Zenphoto functions have meanwhile been changed.

Great news! I am up, running 1.4.10. Thanks everyone for the help, zenphoto is a great program and it has great support.