another problem the computer will not back up?

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I'm not sure which computer you are refering to. I'll asssume you're refering to your new laptop. The laptop must first be associated with an external hard drive so that time machine (the backup software on your computer) can backup everything properly. The first backup takes around an hour or so then much quicker from that point forward. However, you'll have to physically plug in the drive to allow time machine to do its job. You can use the Lacie hard drive you already have to backup the laptop as well as the iMac.

This may be something we need to set up next time we meet.