You need to have a thumb drive / usb key / etc to transfer the files over to your computer. Yes it is a long process, and fairly annoying.
Way 1: If you have a Ubuntu computer that is the same version and architecture (e.g. 64-bit or 32-bit)
1) Open up Synaptic on the computer with Internet access
2) choose to install vnc*
3) Hit apply once (to bring up the confirmation window)
4) Tick the "Download package files only" tickbox
5) Hit apply again (confirming)
6) Wait for it to finish
7) Go to "Places" => "Computer" => "File System" => "var" => cache => "apt" => "archives"
8) Select "View" => "List"
9) Sort by date modified.
10) Copy the latest files to a thumb drive.
11) On the home computer, open up Synaptic again and go "File" => "Add downloaded packages"
12) Go to the folder on the thumb drive with the downloaded files
13) Click open and it should allow you to hit apply to install.
EDIT: You might be able to use aptoncd instead of all the above steps
Way 2: If you cant use way 1
1) Search for the following files on http://packages.ubuntu.com/ and download the right one for your version of Ubuntu (Note: sadly vld requres lots of bits, so it s a long list)
libswscale0
libtwolame0
libavutil49
libxcb-keysyms1
libdca0
libpostproc51
libcddb2
libass4
libavformat52
libdvbpsi5
libx264-85
libschroedinger-1.0-0
libvlc2
libenca0
vlc-nox
libqtcore4
libupnp3
libgsm1
libdvdnav4
libiso9660-7
libdvdread4
vlc
libqtgui4
libavcodec52
liblua5.1-0
libmad0
vlc-plugin-pulse
libmodplug0c2
vlc-data
libtar
libaudio2
libvlccore2
libvcdinfo0
libebml0
libmpcdec3
libmatroska0
libmng1
libmpeg2-4
libsdl-image1.2
libfaad2
liba52-0.7.4
2) Go to the computer and double click the files (you need to guess and check ones that do not depend on others), then hit "install package" and follow the prompts
3) when you have done the last one, (the vlc one - the others were the other programs needed to install vlc) VLC should be installed.
* If you cannot see VNC in synaptic list then:
1) Go to 'Settings" => "Repository"
2) Tick the "Community maintained Open Source Software (universe)" checkbox
3) Click "close" (to apply the settings) and close the dialogue box.
4) Hit "Reload" (to get the new package info).