The details presented in this answer are correct - however other answers do provide workarounds that exist to allow SQL Server to be started in a special mode that allows the server administrator to access SQL Server as a member of the sysadmin role.
Even the most uber-admin type of connection option Dedicated Administrator Connection (DAC), which can only be used as a local connection, and lets you undo all kinds of evil, still requires login credentials. So I don't think there's an official way to do this.
The quickest way to resurrect this system may be to shut down SQL Server, copy the user database files somewhere safe, uninstall, reinstall (making sure to service pack up to at least the level you were previously at), copy the files back and attach the databases. (Not sure the copying out/back is required, but just to be safe...).
You'll still need to manually recover server level objects (e.g. logins)
