1) seems you ran getnewsources before as root? As root delete the file /tmp/inet.log
2) next getnewsources says you have no Internet because it could not access google. This could be a DNS-issue which usualli is resolved by using OpenDNS as indicated, but apparently this didn't help either. Did you successfully download the file getnewsources on the same PC where getnewsources complains about the missing Internet? I assume that despite of all these messages you do have a working Internet connection. If so then
3) as an alternative option you can try to download lomanager
rpm-file and in case you already have java and some other dependencies installed you could then install lomanager by having Synaptic closed, opening a terminal in the directory where you downloaded the package and copy/paste:
apt-get install lomanager-3.3.1-2pclos2011.i586.rpm
and in case it could be installed you can then run it form the menu entry. However, as long as point 2 above is not resolved, lomanager will give you the very same error message and in addition you can not use Synaptic for the same reason. What puzzles me is that in a previous post Synaptic downloaded some repo-sections, so your Internet connection seemed to work.
Anyway, please ensure to have a reliable and working Internet connection on the PC of question.