Philosopher,
Prof. Lindzen has criticized the computer models for some of the reasons you mention. But he agrees that the the data clearly show that the earth has warmed. That evidence is not from computer models but from empirical observation of temperatures all over the world over the past 130 years, and the observed receding of glaciers and sea ice. Satellite imagery adds to the picture for about the past 40 years and pretty much tells the same story.