Component is not physically capable of 1080p. Therefore, there is no way your can activate that resolution on any device. Your going to need some new hardware.
Now apparently, there is a way to achieve 1080i resolution. But I am not sure how to do that. If anyone knows how feel free to drop in another answer. However, since you said in chat that Linux does support it, I am almost positive it is a driver issue. You should try to find information from whatever company you bought the TV from and see if they will supply drivers. If not, make sure all drivers are updated.