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Are you running Leopard? If so, then why not just plug the LaCie drive in, let Time Machine do its backup of everything, and then bring your computer to Apple. If they put a new drive in it, then when you get back home and start it up for the first time, plug the LaCie drive back in and tell it to import all of the Time Machine files. I'm pretty sure you can do this, but correct me if I'm wrong. It would be like using migration assistant on a new Mac to transfer all the files from an older Mac. If the Time Machine restore works like that, then your desktop, user preferences, and everything else will be exactly the same as before you brought it in. This seems like the easiest way. Hope this helps.
 
Eh, just check the size of your home folder, get a USB device big enough and copy it across. If you can't be arsed to clone the whole HDD, that'll take across everything you need - anything outside of your home folder is the system, apps etc. You can migrate your home back again after installation.

As others have said the click of death is a race against time, back up the most important stuff first, then try the full home folder, then if applicable try the full HDD.

Oh and invest in Leopard and a decent external HDD for Time Machine next time ;)
 
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