If you can mount the old partition into the filesystem (I'll use /dev/sda1 for the old partition and /mnt as the mount point in the example), try this:
As a trial run, first use "-avn" as the parameters to rsync. That will list the files the program will transfer but not copy any files. If everything looks okay, run it with just "-av" to create a complete copy of the old home directory tree under the new /home. (You can use Ctrl-C to cancel the dry run midway through once you're sure it will produce the proper results.)
sudo mount /dev/sda1 /mnt
sudo rsync -av . /home
I keep /home on a separate partition so I can change operating systems without losing my files.
Update: Actually this task is best performed after booting into a "recovery mode" session using your new installation. Choose "root shell" when you are presented with a menu of choices. You won't need to use "sudo" as you already have root privileges in recovery mode. However you may need to make the new installation's filesystem writable by running the command:
at the initial shell prompt. Note there is no space between the comma and "rw".
mount -o remount,rw /