I installed ZenPhoto last month and configured it the way I wanted it to look. It ran fine, and still does if I access it a certain way.

I recently transferred the website to my hosted website as an addon domain. If I type the URL this way:
mywebsite.com/folder/zenphoto/page/gallery (where folder contains the addon domain), everything works great. I can see the albums, etc.

However, if I type the URL this way:
addondomain.org/zenphoto/page/gallery then I get the 500 Server error.

I can also get to it this way, bypassing the mod_rewrite rules:
addondomain.org/zenphoto/index.php?page=gallery

So something is going on with .htaccess, or, if I'm reading the docs correctly, it's now zenphoto-rewrite.txt that's doing the .htaccess work.

Do I need to reconfigure something so that it takes the different root into account, or can I modify the zenphoto-rewrite.txt file?

Here's what it currently has:

#### image and album page references
RewriteRule ^%PAGE%/([0-9]+)/?$                         index.php?page=$1 [L,QSA]
RewriteRule ^%PAGE%/([A-Za-z0-9_\-]+)/?$                index.php?p=$1 [L,QSA]
RewriteRule ^%PAGE%/([A-Za-z0-9_\-]+)/([0-9]+)/?$   index.php?p=$1&page=$2 [L,QSA]
RewriteRule ^(.*)/%PAGE%/([0-9]+)/?$                    index.php?album=$1&page=$2 [L,QSA]
RewriteRule ^(.*)/%PAGE%/([A-Za-z0-9_\-]+)/?$       index.php?album=$1&p=$2 [L,QSA]

The rewrite base is wrong now. When you moved the site to another domain or within a folder you should re-run setup. That will update that for you.
http://www.zenphoto.org/news/moving-and-changing-existing-installations

mywebsite.com/folder/zenphoto/page/gallery and addondomain.org/zenphoto/index.php?page=gallery are completely different url. You have to decide which you want to use. You cannot use both, at leat not with modrewrite rewritten urls.

Of the first the rewrite base would be /folder/zenphoto, on the second just /zenphoto. If you install in the root of a domain it is naturally just /.

You can also change the rewrite base manually in the htaccess file.