The horror of having to back up your hard drive via floppies is the reason that alternative interfaces are sometimes provided - like SCSI or USB - either as standard or as expantion options.
Having said that, I think you've found the easiest way already - remove the disc and put it in your PC!
I would have liked to suggest if this happens regularly that you add one of those "removeable disc caddies" to your PC; I have one so that I can fix peoples 3.5" hard discs without dismantling my machine. However, if your K/B hard disc is a 2.5" "notebook" hard disc, then you need an adapter to convert the 44 pin interface/power connector on the 2.5" drive to the 40 pin interface and separate connector used for 3.5" discs. On my PC this was a connector too far and the notebook disc was never recognised when I installed in via the cradle, but it did work when I took the PC to bits and hooked it up (via the adapter) directly to the IDE cable!
Have fun!
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John Allcock