Acquire::http::Proxy "http://123.456.7.8.sg:8080"; is not a command. It is a
line to add to /etc/apt/apt.conf (for instance at the end of it). And I do
not know what is the ".sg" for but it should not be there.
The lines in .bashrc will only have an influence on what you do in a
terminal. If you want to use a graphical front-end to APT (and not apt-get or
aptitude), I believe it will not have any influence.
The configuration through Synaptic's preferences should have worked...
There is something I am not sure about: has APT ever been able to access the
repository from your system and with the same network interface? If it used
to work, configuring a proxy does not look necessary (unless the proxy was
added since then).