How Do I fix my particular broken package system?

Question

So I'm having a bit of trouble with my Ubuntu 13.10 installation. I cannot for the life of me figure out what I did to break it, I think it had something to do with an update not finishing. Anyway, When I got to check for updates or try and install a package I get the following errors:

Updating Software:

THE PACKAGE SYSTEM IS BROKEN
Check if you are using third party repositories. If so disable them, since they are a common source of problems. Furthermore run the following command in a Terminal: apt-get install -f

Installing a package from the repos (in this case compiz, for the sake of example):

dj@ThetaDome:~$ sudo apt-get install compiz
[sudo] password for dj: 
Reading package lists... Done
Building dependency tree       
Reading state information... Done
compiz is already the newest version.
You might want to run 'apt-get -f install' to correct these:
The following packages have unmet dependencies:
 ca-certificates-java : Depends: ca-certificates (>= 20121114) but it is not going to be 
installed
 liblwp-protocol-https-perl : Depends: ca-certificates but it is not going to be installed
 libwww-perl : Depends: ca-certificates but it is not going to be installed
 python-httplib2 : Depends: ca-certificates but it is not going to be installed
 python3-httplib2 : Depends: ca-certificates but it is not going to be installed
E: Unmet dependencies. Try 'apt-get -f install' with no packages (or specify a solution).

This is the result of apt-get -f install:

dj@ThetaDome:~$ sudo apt-get -f install
Reading package lists... Done
Building dependency tree       
Reading state information... Done
Correcting dependencies... Done
The following package was automatically installed and is no longer required:
  libc6-i386
Use 'apt-get autoremove' to remove it.
0 upgraded, 0 newly installed, 0 to remove and 20 not upgraded.
2 not fully installed or removed.
Need to get 183 kB of archives.
After this operation, 0 B of additional disk space will be used.
Get:1 http://us.archive.ubuntu.com/ubuntu/ saucy/main ca-certificates all 20130610 [183 kB]
Fetched 183 kB in 0s (262 kB/s)         
dpkg: error processing ca-certificates (--configure):
 package ca-certificates is not ready for configuration
 cannot configure (current status `half-installed')
dpkg: dependency problems prevent configuration of python3-httplib2:
 python3-httplib2 depends on ca-certificates; however:
 Package ca-certificates is not installed.
dpkg: error processing python3-httplib2 (--configure):
 dependency problems - leaving unconfigured
No apport report written because the error message indicates its a followup error from a previous failure.
       Errors were encountered while processing:
 ca-certificates
 python3-httplib2 
E: Sub-process /usr/bin/dpkg returned an error code (1)

Can anybody please help me resolve this issue? I'd like to troubleshoot through this problem and keep my installation!

What happens when you try to remove one of these packages?

sudo apt-get purge ca-certificates
Reading package lists... Done
Building dependency tree       
Reading state information... Done
You might want to run 'apt-get -f install' to correct these:
The following packages have unmet dependencies:
 ca-certificates-java : Depends: ca-certificates (>= 20121114) but it is not going to be installed
 liblwp-protocol-https-perl : Depends: ca-certificates but it is not going to be installed
 libwww-perl : Depends: ca-certificates but it is not going to be installed
 python-httplib2 : Depends: ca-certificates but it is not going to be installed
 python3-httplib2 : Depends: ca-certificates but it is not going to be installed
E: Unmet dependencies. Try 'apt-get -f install' with no packages (or specify a solution).