Maybe I can help a little here?
Users details are recorded in the nnn_users table (where nnn is the the table prefix of your installation) so you should be able to make your new users table from your 'old' one, i.e. the table with the usernames that you want to migrate across.
-but- please be aware that the first action of an moves to repliate an MySQL table DROPs the existing table and all of it's content is erased. So please backup the table you're moving the data to. Backing up simply by changing its name will work in this instance since your SQL 'dump' should create the table from new.
As Richie says, you need the extract [' dump '] the SQL data for your old users table and insert it into your new site's database.
You can easily do this using phpmysqladmin, but I'll have to admit I can't immediately repeat the steps you need to follow ...because I never use it (I use Navicat), shame on me, eh? ;)
So, you should be able to be able to copy the data from your old database and insert it into your new database quite easily. You might have a hiccups if you have bridged programs installed, but you should be able to iron out those problems if you come across them. If you ahve nothing that is bridged tehn you should be OK.
Hope that helps a little