How do I restore old files from my Time Machine backups of my old MacBook OS X Snow Leopard to my new MacBook Pro in OS X Lion?

I had a MacBook Snow Leopard for 3 years and I used Time Machine to back up my files. Because I was running out of memory on my Macintosh HD and my external HD had a much larger capacity, I started deleting big files. I knew they were backed up in case I needed them, and I often went back to restore them when needed.

I just got a new MacBook Pro with OS X Lion already installed. I used Migrant Assistant (not Set Up Assistant) to restore files, applications, settings, etc from my old MacBook using Time Machine. However, it only restored what was in my latest backup. When I try to restore files from previous backups, I get the message "The folder “xyz” can’t be opened because you don’t have permission to see its contents." Help please. Files I deleted that I want to restore are mostly music and mailboxes.

Thanks a lot!

Joana