This is not an issue. Just make sure you boot from a Live-CD, mount the Filesystems accordingly into 2 Directories like new and old, and copy all files over. I usually use the cp command like this:

~# cd /old
~# cp -aRv * /new

Whan that is done - younneed to fix 2 Things.

• All hard-disk UUID's have changed. Identify these using blkid. Check the FAQ
• Make sure you update the /etc/fstab and /etc/grub/menu.lst files with the UUID. If the fstab entry is wrong, you'll get a Kernel panic - cannot find root-FS. In case the Grub Entry is not fixed, you'll get an error 15, file not found when trying to boot the kernel from the boot-loader

At the end - you have to regenerate the the initial Ramdisk using mkinitramfs. Check the manpage/google for your specific OS Version.
After that - you should be fine booting again.