Well you can remove the "non-free" repository from the sources.list file since that one doesn't exist anymore.
You don't know what will break linspire from that sources.list file, they just point APT to the places where it can find it's software.
basically you do this :
apt-get update (to update the sources, make sure you don't see any errors here).
apt-get install synaptic (this will install synaptic

)
if both 2 commands ended without errors you can start synaptic by typing "synaptic"
now it's possible that the "apt-get install xxx" command gives you some output, that can be following things :
New packages
updated packages
sugested packages
not updated packages
when apt tells you it's gonna update a package it can mean it will trash the system, (like libgc6 will cause trouble).
as long as APT tells you it's gonna : Install 1 new package, and leave 514packages not updated chances of trashing the system are minimal.
Hope this is a bit clear for you (I made a more detailed post here in another thread explaining why APT might cause trouble on Linspire).