Install Webmin on your server and log into Webmin using https://www.yourserver.com:10000/ (or use https://xxx.xxx.xxx.xxx:10000/ where the xxx's are your internal IP address). Under servers you should see "PostgreSQL Database Server".
Select that and then your Wikidot database. Open the "site" table and then "View Data". Find your site that you set private, edit the record and change the private field to "f" (for false). Save the changes and you should be able to get back in.
Once you're up and running again, you should create a system:join page that consists of this code:
Please change this page according to your policy (configure first using [[[admin:manage|Site Manager]]]) and remove this note.
+ Who can join?
You can write here who can become a member of this site.
So you want to become a member of this site? Tell us why and apply now!
Or, if you already know a "secret password", go for it!
This is based on an older revision of WDOS (rev 393), so things might have changed in newer versions. Webmin is a great tool for remotely managing small changes in the wikdidot database. Hope this helps.