I used to be Domino certified .... stuffed if I like it now! Doesn't come close to a good database app and email system (seperate).
Anyway, if you hold down shift, click view and "show server names" it will show you the paths/names for all the databases in use.
But, the only good thing about Notes is its portability. As someone said above, just copy the Notes directory and all its subs and then copy the notes.ini. Put all this is the same directory structure/location as the source system and you should be good to go
edit: Now this is a bit "out there" but, its also unlikely but possible that you may need to copy your hosts and lmhosts files. There is a very minimal chance that the servers your connecting to are not on your DNS server. Neither of the files have an "." extension and are just called "hosts" and "lmhosts". Take a look at these in notepad and see if you see anything similar to:
192.168.1.1 LONSERVER
The numbers and name will be diferent but any entries in there in this format may need to be copied to your new computers Hosts and LMHosts ..... these two files live in your windows\system32\drivers\etc directory. (Usualy c:\windows....) These changes are dynamic and no reboot is needed so you can experiment with these quickly to resolve any issues. When you see the server names by using the option in Notes, you should be able to look for the existance of these in your Hosts and LMhosts.
edit2: Note, the Notes.ini can actually be located anywhere on the search path. We have in the past had a lot of the Notes stuff (including Notes.ini) on a server drive. Best use the Windows Search function when trying to locate this, once you do, look in this directory and see if any other Notes files are in the same location.