From backups of old server to new server – migration?

How hard would it be to install a backup of wordpress and its database to a different server? The catch is, The original server is no longer available. You have the complete files and a mysql backup to work with. The original home directory was /var/www/wordpress and probably have to be changed to /.

I have the database re-installed and also wordpress files. I can view the frontpage but cannot access wp-admin. Its a paths issue. Edit the database somehow?

Thanks,