Hi Patrick,
Here is a discussion on cleaning the sensor of a Canon DSLR: http://www.dpreview.com/forums/thread/2988797
However, I would get in contact with Canon right away and would explain what happened. They would surely know what to do next and would also be able to tell you a price for a possible repair.
Another way of fixing the issue (however, you would need to know how to do it - practically and technologically) is to get you a broken T2i with a working sensor and replace the sensor. See, for example, here: http://www.ebay.com/sch/i.html?_odkw=canon+sensor&_osacat=0&_from=R40&_trksid=p2045573.m570.l1313.TR0.TRC0.H0.Xcanon+T2i+as+is.TRS0&_nkw=canon+T2i+as+is&_sacat=0
I hope this helps.
Steffen