I'm thinking your boot partition is full of old kernel images, leaving no room for the new one apt-get is trying to install. You can type
dpkg -l linux-headers-\* linux-image-\* | grep ^ii
into a terminal window. When I do this, I get
ii linux-headers-3.8.0-18 3.8.0-18.28 all Header files related to Linux kernel version 3.8.0
ii linux-headers-3.8.0-18-generic 3.8.0-18.28 amd64 Linux kernel headers for version 3.8.0 on 64 bit x86 SMP
ii linux-headers-3.8.0-19 3.8.0-19.30 all Header files related to Linux kernel version 3.8.0
ii linux-headers-3.8.0-19-generic 3.8.0-19.30 amd64 Linux kernel headers for version 3.8.0 on 64 bit x86 SMP
ii linux-headers-3.8.0-21 3.8.0-21.32 all Header files related to Linux kernel version 3.8.0
ii linux-headers-3.8.0-21-generic 3.8.0-21.32 amd64 Linux kernel headers for version 3.8.0 on 64 bit x86 SMP
ii linux-headers-3.8.0-22 3.8.0-22.33 all Header files related to Linux kernel version 3.8.0
ii linux-headers-3.8.0-22-generic 3.8.0-22.33 amd64 Linux kernel headers for version 3.8.0 on 64 bit x86 SMP
ii linux-headers-3.8.0-23 3.8.0-23.34 all Header files related to Linux kernel version 3.8.0
ii linux-headers-3.8.0-23-generic 3.8.0-23.34 amd64 Linux kernel headers for version 3.8.0 on 64 bit x86 SMP
ii linux-headers-3.8.0-25 3.8.0-25.37 all Header files related to Linux kernel version 3.8.0
ii linux-headers-3.8.0-25-generic 3.8.0-25.37 amd64 Linux kernel headers for version 3.8.0 on 64 bit x86 SMP
ii linux-headers-generic 3.8.0.25.43 amd64 Generic Linux kernel headers
Since I have quite a few, I could delete some of the oldest with
sudo apt-get remove linux-headers-3.8.0-18
If apt-get fails because it misses some package dependencies (which you can't install due to the lack of free inodes), you can resort to dpkg directly instead:
sudo dpkg --remove linux-headers-3.8.0-18
Do that a couple of times to your oldest linux-headers-* and you should have room.