A SQL Server database backup/restore issue
If you have a copy of the master database which holds the DBBackupEncryptCert then you'll want to restore that and grab the copy of the certificate, then import it into your current instance for use.


  If there is a way we can restore this database using the current encrypted backup without the certificate key ...


That would defeat the whole purpose of encrypting the backup - so, unfortunately, the answer is that there is no way. There is no back door or gated access to get the data, it is encrypted by the certificate of which no one has a copy but you. That's what makes it safe and secure (well, partially).


  We also have a one-week earlier non-encrypted backup of the database.


Without the certificate, this is what you're going to be able to recover.