Having had the fortune to have visited Tibet I can tell you that the Dalai Lama is the most revered person in the lives of ordinary Tibetans, they see him as the head of State and their spiritual leader. Unfortunately Tibet is no longer recognised by the UN as an official country instead as a province of China. With regard to the Panchen Lama it is believed that Gendun Choekyi Nyima who was officially recognised by the Dalai Lama as the reincarnation of the 11th Panchen Lama in 1995 is being held along with his family by Chinese authorities in Beijing under "protective custody" the Chinese Government have said that the faimly of Gendun Choekyi Nyima asked to be protected as they feared he would be killed by the Tibetan people. China then chose another 6 year old, Gyaltsen Norbu, as the Panchen Lama. Nobody knows for sure where the "official" Panchen Lama is, but I believe a fairly hefty reward has been raised for information leading to the discovery of his whereabouts. I don't think it's a case of the West not caring as such but China, but that the consequences of opposing China on this matter [and many others] are greatly exceed by the benefits of building trade relationships with them. As for the history of Tibet, there's detailed account of Tibetan history here:
http://omni.cc.purdue.edu/~wtv/tibet/history.html#iif01 maybe you can judge for yourself whether China have a legitimate claim over the country.