Ubuntu – recover LVM after hdd crash

[EDIT: If you are unfamiliar with LVM, please read this overview or at least the Wikipedia page about it.]

LVM splits its Physical Volumes in slices called "Physical Extents" (PE). You can check which Logical Volumes have PEs allocated in the PVs that you still have by issuing this command:

pvdisplay -m

Which outputs something like this (showing one PV here only):

--- Physical volume ---
  PV Name               /dev/sda3
  VG Name               htpcvg
  PV Size               929.27 GiB / not usable 18.71 MiB
  Allocatable           yes 
  PE Size               32.00 MiB
  Total PE              29736
  Free PE               1190
  Allocated PE          28546
  PV UUID               7SfjbY-3dy4-UDeB-iSEL-3R9Y-vvnv-O7m9jr

  --- Physical Segments ---
  Physical extent 0 to 28545:
    Logical volume      /dev/htpcvg/home
    Logical extents     29430 to 57975
  Physical extent 28546 to 29735:
    FREE

With this info you can know how much of your LVs is stored in that PV.

Then, if that information shows that you have some extents of your LVs' available, you can activate the VG that contains them with this other command (edit VolGroupName): [EDIT: Please read the manpage]

vgchange -a y --partial VolGroupName

That should make your LVs "available", but faulty anyway (you won't be able to read missing PEs, obviously). To be safe, you could also make your defunct LVs read-only with lvchange -p r --partial /path/to/logical/volume

Now, given that you probably won't be able to mount the filesystems that reside in your partial LVs, you should copy what's left of them with ddrescue:

ddrescue -n /dev/mapper/yourVG-yourLV /file/for/the/dump ddrescue.log

And then do some forensic analysis on that dump. Here you have many options. Photorec is just one.

It looks like you're trying to add a new primary partition in-between your current /dev/sda1 and /dev/sda2. (Evidence: fdisk is saying that the acceptable ranges of end points are 499712-501757, default 501757, which is between those two partitions.) There simply isn't enough space there to do that. Instead, tell fdisk to begin the partition at 104855552 (or later) and give it the default end value (unless you want to save some space for some other purpose). This should give you a partition that uses the rest of the available disk space, minus a bit of wastage near the beginning.

Alternatively, you could use cfdisk, GParted, or some other tool that provides a more visual approach to partitioning, which will make such an error less likely.