Crashing right after update (no Error)

[goomba_stomper]

I am currently trying to set up a tekkit Lite server and my server is running fine but my computer will not run Tekkit Lite. Every time I hit the log in button it will go fine until it says looking for updates and then just closes with no warning. I have looked at other threads saying that I need to use Java 1.6 instead of 1.7 (which I have) but I have not been able to find a way to get java 1.6 on my computer. + how do I run 1.6 and 1.7 at the same time so I can run the server and play Tekkit Lite.