transferring a huge amount of files

I have this old computer that hardly turns on anymore.  It's a trooper, but it's gotta go.

Years ago we bought a backup system--you're supposed to be able to back up all the files on one computer and vomit all the files onto a different computer.

Well, I have the new computer, a windows machine I got inexpensively at Fry's.  So we're trying to get the backup system to vomit all the files into the new computer, and it's not working.

I'm worried the backup system is a lemon and we should just get a portable harddrive to put all the files onto and transfer them that way.

But it's a shit ton of files.  I think it would take days to transfer them all.  Weeks?

ps  How do I make people mix cds if I don't have a cd drive anymore?  How do the kids do that nowadays?