Did violence solve the Civil War?

The previous answer discusses one interpretation of the question: did violence address the root causes of the Civil War? But the question could be read another way: was violence the primary reason that the North emerged victorious?

The short answer is: not entirely.

For starters, the population of the North outnumbered that of the South by a factor of three to one. Robert Krick, a historian and author, cites this as the primary determinant of the war's outcome: more people meant more soldiers, more productivity, more industry, and more money to finance the North's war efforts. 

Related to this was the Confederacy's inability to gain international recognition. Without finances and support from foreign governments, particularly the Europeans, the South was denied access to a variety of resources that could have sustained them against the North's superior numbers.

Finally, the South became politically fractured as the war went on. Noah Andre Trudeau, an author of several Civil War analyses, puts it this way:

Ask the question, “What was the South fighting for; what was the Southern way of life that they were trying to protect?” and you will find that Southerners in Arkansas had a very different answer from Southerners in Georgia or Southerners in Virginia. 

Compare this to Lincoln's simple message of preserving the Union, and you begin to see how Southern morale could falter.

Of course, none of these factors would have mattered without violence. The Civil War was, after all, a war,  the deadliest war for U.S. soldiers in our history. And violence did play a role in the South's eventual loss. Opinions are divided as to the precise strength of the respective armies and exact competence of the armies' respective leaders, but irrespective of whether the South was somehow superior in military capability, the North fought and won enough to allow their other accumulated advantages to take their toll. Gary Gallagher, a professor of history at Penn State, said the following:

The principal cause of Confederate failure was the fact that the South’s armies did not win enough victories in the field–especially enough victories in a row in the field–to both sustain Confederate morale behind the lines and depress Union morale behind the lines.

The Confederate armies did win several battles, including the first and second battles of Bull Run, but tides began to shift when southern forces were driven out of Maryland in the battle of Antietam.

In summary: Without violence, the Civil War might not have been resolved. But violence alone cannot account for the Civil War's final resolution.