Comment Upgrade kernel + R1Soft (Score 3, Informative) 300
Just upgrade your kernel using a manual build of the 2.6 kernel.
Also install static versions of the modutils ( insmod, modprobe, etc )
Use an external ( a machine with decent software ) for this so your compile doesn't break.
I have done so in the past and it works fine. ( and plan an update for those machines, anything with 2.4 is way to old... )
After that you can just use R1Soft hot copy,
http://www.r1soft.com/tools/linux-hot-copy/
This program is free ( as in beer ) to download and works with every block device.
You can even write to a block device if you really need to.
Their commercial offerings are pretty good as good. ( and DO work with the 2.4 kernel )
We use it here at work.
I heard btrfs supports something like this as well.
Any way, good luck!