First off, the Civil War went a lot deeper than slavery. Ever since the foundation of the United States of America, there was enmity between the North and the South. The two regions had radically different cultures, which made it hard for them to get along. The South had a much smaller population, fewer large cities, and was overall rural. The North was full of harbors with large cities, industrialization, and dense urban areas. This caused tension from the very beginning.
The South wanted very low tariffs because of their agricultural economy while the North wanted high tariffs to protect their products from cheaper European products. The South generally did not want to get rid of slavery, while the North quickly abolished it. In fact, if the Constitution had disallowed slavery, it is extremely unlikely that the South would have joined. One of the first acts of all of the Northern states after the ratification of the Constitution was to abolish slavery. They planned to slowly wean the South off of slavery, first by abolishing the importation of slaves after 1807. However, the South was unwilling to abolish slavery because that was the lifeblood of its economy.
Until the Emancipation Proclamation in 1863, the war was primarily over taxation. The South believed they were being treated unfairly and decided to get out of the Union and form their own Confederacy. Of course, the North didn't want that.
Why didn't blacks fight? Well, first off they were slaves. They had no weapons or communication systems. They couldn't just say, "everyone take over your plantation on March 18 at midnight". John Brown wanted to create an uprising of slaves like that, but it failed and he was hung.
So, the war wasn't really completely about slavery. It was over the deep cultural differences of the North and the South. Although the focus was turned to slavery later in the war, the slaves had very little chance to fight (especially because blacks weren't even allowed to fight in the Union for the first part of the war).