This may help, as I was having the same issue with the same version of Ubuntu. Upgraded to latest Technic on 3 Windows machines no problem. Updated Ubuntu to latest Java as well, same problem. Tried removing everything that had to do with Technic launcher including .techniclauncher directory and re-downloading. Still getting same problem.
Then I found http://askubuntu.com/questions/100751/minecraft-in-jdk-1-7-0-u2-x64 and tried the script there except for the launcher and fixing the path for the current Java I have installed, and it got me past the Mojang logo this time. There's also instructions in that link to update
lwjgl which I haven't tried yet but that may also help.
Now though apparently there are item or block ID conflicts...that never happened before so I'm trying to figure that out. When I click on "automatically assign an ID" or any other option on the screen, but nothing happens.
