My PS3 died of YLOD, how can I keep my gamesaves?

I have a full hdd-backup on a external hdd , can I restore my new PS3 slim with my backup? I need my gamesaves, and wonder how I can do it? My old PS3, is a 60 gigabyte FAT, I took a full backup and wonder if the backup can be used to my new PS3 slim? I have heard about something like "your external hdd needs to be formatted as FAT32. only these discs are recognisable." What do I need to do? Tanx 4 all answers!