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This question already has an answer here:

These are the updates:

-Safe and easy web browser from Mozilla firefox
-Safe and easy web browser from Mozilla- Unity menubar integration firefox-gobalmenu
-Safe and easy web browser from Mozilla-GNOME support firefox-gnome-support
-Linux kernal image for version 3.5.0 on 32 bit x86 SMP linux-image-3.5.0-gereric (New install)

And this is the output:

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

Details:

The following packages have unmet dependencies: 

linux-image-generic-lts-quantal: Depends: linux-image-3.5.0-26-generic but it is not installed
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marked as duplicate by Eliah Kagan, Thomas Ward, Eric Carvalho, Basharat Sialvi, Seth Apr 5 '13 at 3:25

This question was marked as an exact duplicate of an existing question.

    
If you can, upload all the output that you get into paste.ubuntu.com and then link it here. Also, take a look at How do I resolve unmet dependencies? – Lucio Apr 4 '13 at 23:40
    
Finally, tell us what you get entering sudo apt-get install linux-image-3.5.0-26-generic in a terminal. – Lucio Apr 4 '13 at 23:41
    
Welcome to Ask Ubuntu! This question will probably be closed as a duplicate soon. If those answers don't fully address your question please edit it to include why and flag this for re-opening. Thanks! – Seth Apr 5 '13 at 3:25

a few simple things I would try when this happens: (but I am not an expert...)
- click the Check button again before clicking the install updates button.
- disable ppa's that cause problems (I don't know whether you use a ppa for linux-image-generic-lts-quantal?)
- chose an other Download server under update manager -> settings -> ubuntu Software -> download from:

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