I am getting the same error message ("Setup did not detect a working mod_rewrite facility."). I manage my server so I can enable whatever is required to fix it...
This is the current situation.
core prefork http_core mod_so mod_auth_basic mod_auth_digest mod_authn_file mod_authn_alias mod_authn_anon mod_authn_dbm mod_authn_default mod_authz_host mod_authz_user mod_authz_owner mod_authz_groupfile mod_authz_dbm mod_authz_default util_ldap mod_authnz_ldap mod_include mod_log_config mod_logio mod_env mod_ext_filter mod_mime_magic mod_expires mod_deflate mod_headers mod_usertrack mod_setenvif mod_mime mod_dav mod_status mod_autoindex mod_info mod_dav_fs mod_vhost_alias mod_negotiation mod_dir mod_actions mod_speling mod_userdir mod_alias mod_substitute mod_rewrite mod_proxy mod_proxy_balancer mod_proxy_ftp mod_proxy_http mod_proxy_ajp mod_proxy_connect mod_cache mod_suexec mod_disk_cache mod_cgi mod_version mod_php5
.htaccess
# htaccess file version 1.4.5;
# Rewrite rules are now handled by PHP code
# See the file "zenphoto-rewrite.txt" for the actual rules
#
# These rules redirect everything not directly accessing a file to the Zenphoto index.php script
#
<IfModule mod_autoindex.c>
IndexIgnore *
</IfModule>
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /
RewriteCond %{REQUEST_FILENAME} -f [OR]
RewriteCond %{REQUEST_FILENAME} -d
RewriteRule ^.*$ - [L]
RewriteRule ^.*/?$ index.php [L,QSA]
Any ideas, please?