Minecraft Instance fails restart. Failed to start AMP. Exit code was 0

Solution follows for anyone who needs it:

Ubuntu by default does not allocate all space and uses LVM as Mike suspected. GParted is not enough to expand the disk.
Steps to expand the disk: (NOTE: I am on VMWare and had already allocated more raw disk space to the Ubuntu server running AMP.)

  1. Check for free space with vgdisplay
  2. Check the logical volume size with lvdisplay
  3. Expand the logical volume to 100% of free space using lvextend -l +100%FREE /dev/ubuntu-vg/ubuntu-lv and run lvdisplay to verify the change.
  4. Run df -h to verify the root file system then resize2fs /dev/mapper/ubuntu--vg-ubuntu--lv and finally df -h to verify that the space has indeed changed.
    Source: Ubuntu: Extend your default LVM space - Packet Pushers