Understanding Mechanisms of Acquired Resistance to BIBW2992

* Participants will take tablets of BIBW 2992 once a day during each cycle. Each cycle is 28 days (4 weeks). * Participants will come to the clinic on Day 1, 8 and 15 of Cycle 1. For Cycle 2 through 8, they will need to come to the clinic on Day 1. After Cycle 8, they will have study visits every 2 months. * The following tests and procedures will be performed at these clinic visits: physical examination, routine blood tests, research blood samples, EKG (every fourth cycle starting cycle 5), ECHO or MUGA (every fourth cycle starting cycle 5), an assessment of the tumor by CT or MRI scan (every 8 weeks). * Participants may continue to participate in this research study as long as their tumor does not grow and their disease does not worsen and they do not have any severe side effects. * Participants will have a tumor biopsy performed at the end of their participation in this study if their tumor is growing or if they have a new tumor. The purpose of this biopsy is to assess for the presence or the absence of the mutation T790M.