It isn't accurate to say the sun has no impact on Earth. There are four seasons on a normal Earth. There are also tides due to the Moon. But, that doesn't mean the Moon will cause or not cause global warming.
NOAA does a good job of explaining the relationship between Earth and the Sun.
The graph above shows the drastic difference in Earth's gaseous atmosphere regarding carbon dioxide both current and historic. The graph alone shows the drastic change in CO2 levels. But, for some that might not be enough.
...Changes in the "tilt" of the earth can change the severity of the seasons - more "tilt" means more severe seasons - warmer summers and colder winters; less "tilt" means less severe seasons - cooler summers and milder winters. The earth wobbles in space so that its tilt changes between about 22 and 25 degrees on a cycle of about 41,000 years. It is the cool summers which are thought to allow snow and ice to last from year to year in high latitudes, eventually building up into massive ice sheets. There are positive feedbacks in the climate system as well, because an earth covered with more snow reflects more of the sun's energy into space, causing additional cooling. In addition, it appears that the amount of Carbon Dioxide in the atmosphere falls as ice sheets grow, also adding to the cooling of the climate. The earth's orbit around the sun is not quite circular...
Now, 22 to 25 degrees change in the tilt of Earth doesn't mean that tilt is permanent, it means it meanders through that tilt. If Earth changed it's tilt 22 to 25 degrees every 41,000 years we would be in a far different attitude than we are today. But, still 22 to 25 degrees is still significant.
