I had Ubuntu installed on an external HDD and was enjoying it, but my computer was a little slow. I checked my processes and found out that KDE (which I had previously installed) was running its desktop in the background while I was using Unity. I didn't want KDE anymore anyway, so I ran the command sudo apt-get remove kubuntu-desktop and then sudo apt-get autoremove. Everything seemed to be working fine, but when I tried to run sudo apt-get update later, it said that it couldn't remove the lock file because the directory was read-only.
Distraught, I tried deleting the lock file manually but was again met with the read-only error. I tried remounting my drive but I was again told that the drive could only be mounted as read-only. I tried rebooting, but now I can't boot into the hard drive. I can see the (only) partition for the drive on Windows' partition manager. Is there a way to make my hard drive readable and writeable again? If not, is there a way for me to save some of my data?
Edit: Output of sudo lsblk -o name,mountpoint,label,size,fstype;sudo parted -l
Note: The hard drive I have Ubuntu installed on is a Toshiba hard drive that at the time was plugged into my USB 3.0 port.
NAME   MOUNTPOINT                               LABEL               SIZE FSTYPE
sda                                                               465.8G 
├─sda1                                          Recovery            400M ntfs
├─sda2                                          ESP                 300M vfat
├─sda3                                                              128M 
├─sda4                                          Acer              447.6G ntfs
├─sda5                                                              350M ntfs
└─sda6                                          Push Button Reset    17G ntfs
sdb                                                               465.8G 
├─sdb1 /media/ubuntu/11cf8549-8a06-429d-92f6-18                     487M ext2
├─sdb2                                                                1K 
└─sdb5                                                            465.3G LVM2_me
  ├─ubuntu--vg-root
  │                                                               464.3G ext4
  └─ubuntu--vg-swap_1
                                                                      1G swap
sdc                                                                 3.8G 
└─sdc1 /cdrom                                   UBUNTU LIVE         3.8G vfat
loop0  /rofs                                                        1.4G squashf
Model: ATA WDC WD5000LPVX-2 (scsi)
Disk /dev/sda: 500GB
Sector size (logical/physical): 512B/4096B
Partition Table: gpt
Disk Flags: 
Number  Start   End    Size    File system  Name                          Flags
 1      1049kB  420MB  419MB   ntfs         Basic data partition          hidden, diag
 2      420MB   735MB  315MB   fat32        EFI system partition          boot, esp
 3      735MB   869MB  134MB                Microsoft reserved partition  msftres
 4      869MB   481GB  481GB   ntfs         Basic data partition          msftdata
 5      481GB   482GB  367MB   ntfs                                       hidden, diag
 6      482GB   500GB  18.3GB  ntfs         Basic data partition          hidden, diag
Model: TOSHIBA External USB 3.0 (scsi)
Disk /dev/sdb: 500GB
Sector size (logical/physical): 512B/512B
Partition Table: msdos
Disk Flags: 
Number  Start   End    Size   Type      File system  Flags
 1      1049kB  512MB  511MB  primary   ext2         boot
 2      513MB   500GB  500GB  extended
 5      513MB   500GB  500GB  logical                lvm
Model: SCSI SG 1.8.1.7.0 2+6 (scsi)
Disk /dev/sdc: 4035MB
Sector size (logical/physical): 512B/512B
Partition Table: msdos
Disk Flags: 
Number  Start   End     Size    Type     File system  Flags
 1      1049kB  4035MB  4034MB  primary  fat32        boot, lba
Model: Linux device-mapper (linear) (dm)
Disk /dev/mapper/ubuntu--vg-root: 499GB
Sector size (logical/physical): 512B/512B
Partition Table: loop
Disk Flags: 
Number  Start  End    Size   File system  Flags
 1      0.00B  499GB  499GB  ext4
Model: Linux device-mapper (linear) (dm)
Disk /dev/mapper/ubuntu--vg-swap_1: 1074MB
Sector size (logical/physical): 512B/512B
Partition Table: loop
Disk Flags: 
Number  Start  End     Size    File system     Flags
 1      0.00B  1074MB  1074MB  linux-swap(v1)
Edit 2: I can now boot into the hard drive, but it boots into the ash terminal.
Edit 3: Image of shell https://drive.google.com/file/d/0B3JT195D9TgsVXJnekxSOGR6R1U/view?usp=drivesdk
 
     
    