A part of the complete data on the collision became public:
CERN makes public first data of LHC experiments (press release)So far, what we're given are just the high-level data from Run B in 2010. Recall that the center-of-mass energy was \(7\TeV\) at that time.
CMS releases first batch of high-level LHC open data (an extra CERN news article)
OpenData.CERN.CH (CMS subset, policies)
The data is being released under the Creative Commons CC0 status. You will probably need Root, a standard experimental particle physics software framework, to analyze much of the data.
The amount of data and even the data types is large and I won't try to reproduce it here. It would be cooler if we had the access to the newest 2012 collisions, too.
But if you believe that the physicists are severely limited and there is an overlooked way to discover something cool in the 2010, you may have everything that you need to prove that your idea is ingenious.