Imagine that your "/" partition is an LVM and it is corrupted. You need to perform an fsck inorder to boot the system.
Now, get a live CD and boot your system to live cd.
1) Check if lvm2 packages are installed. Else, you can install it via yum.
2) Run the command "fdisk -l" to see if the harddisk partitions are detected.
3) Run pvscan to scan all disks for physical volume. This to make sure that the LVM harddisk is detected by Centos.
PV /dev/sda2 VG VolGroup00 lvm2 [74.41 GB / 32.00 MB free]
Total: 1 [74.41 GB] / in use: 1 [74.41 GB] / in no VG: 0 [0 ]
4) After that run vgscan to scan disks for volume groups.
Reading all physical volumes. This may take a while...
Found volume group "VolGroup00" using metadata type lvm2
5) Activate all volume groups available.
# vgchange -a y
2 logical volume(s) in volume group "VolGroup00" now active
6) Run lvscan to scan all disks for logical volume. You can see partitions inside the hard disk now active.
ACTIVE '/dev/VolGroup00/LogVol00' [72.44 GB] inherit
ACTIVE '/dev/VolGroup00/LogVol01' [1.94 GB] inherit
7) Mount the partition to any directory you want, usually to /mnt
# mount /dev/VolGroup00/LogVol00 /mnt
8) You can access the partition in the /mnt directory and can backup your data