You cannot export a database unless you can get mysql to run. If you cannot get mysql to run on your server for some reason a last resort would be to copy the database subdirectory in it's entirety to another system, and try to export it there. This may or may not be successful. You'd need to create the database first on that server, then copy the directory over the one created by creating the database. I don't know if it'll work or not for you; there are many variables involved in whether or not it will work.
Best recommendation: hire a seasoned administrator to recover it for you.
Jeff