Ultra minor nit-pick, but your account number was stored in a registry entry (HKEY_LOCAL_MACHINE\SOFTWARE\Battle.net\Configuration), not a file.

The account number consisted of four parts:

  Registration Version: This was always 1 for all the account numbers that I still have lying around.
  Registration Authority: I don't actually remember what this was used for.
  Client ID: The actual account number.
  Client Token: Random number used to verify the validity of the Client ID.