I did so, now inside a chroot because the network drivers don't work anymore. apt-get update works as expected, the output of the other commands below:

# env LANGUAGE=en_US apt-get install -f
Reading package lists... Done
Building dependency tree       
Reading state information... Done
Correcting dependencies... Done
The following packages were automatically installed and are no longer required:
  efibootmgr secureboot-db shim
Use 'apt-get autoremove' to remove them.
The following extra packages will be installed:
  linux-image-3.13.0-24-generic
Suggested packages:
  fdutils linux-doc-3.13.0 linux-source-3.13.0 linux-tools
Recommended packages:
  grub-pc grub-efi-amd64 grub-efi-ia32 grub lilo
The following packages will be upgraded:
  linux-image-3.13.0-24-generic
1 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.
118 not fully installed or removed.
Need to get 0 B/15,0 MB of archives.
After this operation, 1.024 B disk space will be freed.
Do you want to continue? [J/n] 
(Reading database ... 205799 files and directories currently installed.)
Preparing to unpack .../linux-image-3.13.0-24-generic_3.13.0-24.47_amd64.deb ...
Done.
Unpacking linux-image-3.13.0-24-generic (3.13.0-24.47) over (3.13.0-24.46) ...
dpkg: error processing archive /var/cache/apt/archives/linux-image-3.13.0-24-generic_3.13.0-24.47_amd64.deb (--unpack):
 unable to make backup link of `./boot/vmlinuz-3.13.0-24-generic' before installing new version: Operation not permitted
dpkg-deb: error: subprocess paste was killed by signal (Broken pipe)
Examining /etc/kernel/postrm.d .
run-parts: executing /etc/kernel/postrm.d/initramfs-tools 3.13.0-24-generic /boot/vmlinuz-3.13.0-24-generic
run-parts: executing /etc/kernel/postrm.d/zz-update-grub 3.13.0-24-generic /boot/vmlinuz-3.13.0-24-generic
Errors were encountered while processing:
 /var/cache/apt/archives/linux-image-3.13.0-24-generic_3.13.0-24.47_amd64.deb
E: Sub-process /usr/bin/dpkg returned an error code (1)


# env LANGUAGE=en_US apt-get clean
#

# env LANGUAGE=en_US apt-get -f upgrade
Reading package lists... Done
Building dependency tree       
Reading state information... Done
Correcting dependencies... Done
Calculating upgrade... Done
The following packages were automatically installed and are no longer required:
  efibootmgr secureboot-db shim
Use 'apt-get autoremove' to remove them.
The following packages will be upgraded:
  linux-image-3.13.0-24-generic
1 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.
118 not fully installed or removed.
Need to get 15,0 MB of archives.
After this operation, 1.024 B disk space will be freed.
Do you want to continue? [J/n] 
Get:1 http://de.archive.ubuntu.com/ubuntu/ trusty-updates/main linux-image-3.13.0-24-generic amd64 3.13.0-24.47 [15,0 MB]
Fetched 15,0 MB in 22s (665 kB/s)                                                                                                                                                                                   
(Reading database ... 205799 files and directories currently installed.)
Preparing to unpack .../linux-image-3.13.0-24-generic_3.13.0-24.47_amd64.deb ...
Done.
Unpacking linux-image-3.13.0-24-generic (3.13.0-24.47) over (3.13.0-24.46) ...
dpkg: error processing archive /var/cache/apt/archives/linux-image-3.13.0-24-generic_3.13.0-24.47_amd64.deb (--unpack):
 unable to make backup link of `./boot/vmlinuz-3.13.0-24-generic' before installing new version: Operation not permitted
dpkg-deb: error: subprocess paste was killed by signal (Broken pipe)
Examining /etc/kernel/postrm.d .
run-parts: executing /etc/kernel/postrm.d/initramfs-tools 3.13.0-24-generic /boot/vmlinuz-3.13.0-24-generic
run-parts: executing /etc/kernel/postrm.d/zz-update-grub 3.13.0-24-generic /boot/vmlinuz-3.13.0-24-generic
Errors were encountered while processing:
 /var/cache/apt/archives/linux-image-3.13.0-24-generic_3.13.0-24.47_amd64.deb
E: Sub-process /usr/bin/dpkg returned an error code (1)