spiffychick wrote: If we did delete the database from the website server itself, would the Board still exist out there in cyberspace for "members" who have gotten onto it?
The board as such would not exist and nobody would be able to access it. However it is possible that it may still show up in search engines for some time to come. There are procedures to have links removed from search engines but they are not simple to do and you would have to do each and every search engine individually.
spiffychick wrote:Could you supply a new admin login to the organization so that they can actually get rid of the Board altogether?
Nobody from here is able to do that - it can be done but only if you have direct access to the database.
Probably the easiest way to achieve what you are trying to do is via your hosts - although they may be reluctant without some authorisation from the account holder. Presumably somebody is paying for the hosting now - if they stop paying then the host will eventually delete the account and your board will disappear.