They should be able to locate it by looking at the config files for the current site - did you point them to where the current (PHP?) code is located?

Without further details, I'll add maybe yes and maybe no; the "location" of the database server is really going to depend on how the hosting is set up.

For example, if your hosting plan is a dedicated server (which I'm guessing is the case, if you can give root access,) in most cases the mysql server is directly on the same machine. No database server should be required as the database server is "localhost." Depending on the API (perl, php, whatever) if you don't specify a database server it will default to localhost.

A caveat, if your ISP says you have mysql services, and the database server is localhost, you have to make sure the mysql server is actually running; you would do this by enabling the service via your control panel or via the server startup options (the second part beyond my expertise.)

However, as said, sometimes the database server needs to be specified as it may be remote. For example, some VDS/VPS plans, and most shared hosting plans, have the database server on a completely different machine or as a "virtual" server, such as mysql.sharedhost12345.com or whatever.

So, the short answer is, if it's not a localhost, you should be able to get a definite answer from any hosting control panel you may have or just ask the ISP hosting your server.

Yes, I have a dedicated server. I believe the developer who originally set my site and database up, did not configure it using the control panel.

The site uses perl scripts and I know that a backup is taken of the follwing directories if this helps?

/etc/httpd/conf
/home/default/example.com/user/htdocs
/var/lib/mysql