Ubuntu – What’s wrong with the ext4 partition

There are a few things going on here. gparted reports the actual used/free space. The kernel reduces the available count by the reserved space. After you removed the reserved space, the free count did not change because the reserved blocks already were free; it is just that non root users are not allowed to invade that space to prevent them from causing trouble by filling up the disk. The gnome numbers are a little flaky because of a bug. Instead of reporting the used space that the kernel reports ( and df shows ), it computes it by subtracting the free space from the total. This causes it to show reserved space as used.

The missing 4GB is actually used is the fs overhead for ext4. NTFS only initially allocates a small amount of space for the MFT, and grows it as needed. The ext series of filesystems though, allocate space for the inode table ( rough equivalent of the MFT ) at format time and it can not grow. The space missing from the reported total space is the inode table. The remaining bit of used space is from the journal ( usually 128 mb ) and resize inodes.

[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.