What factors led to regional economic transformations in the United States from 1854 to the election of Abraham Lincoln as President?
It depends largely on where you were at in that time frame, the South, the Northeast, or the frontier, so let's look at it from those three perspectives. Keep in mind these are only some of the factors you are looking for, as this is a very wide open question.
Northeast - The railroad and the telegraph would be two major factors influencing and transforming the regional economy at this time. The railroad network had grown quite extensive by this time, strengthened by the Bessemer Process, which fostered the creation of new towns, and it made migration and trade much easier, giving factories in New York a way to ship goods all over New England, as well as getting the raw materials they needed to operate more cheaply and efficiently. The telegraph wires (which now crossed the Atlantic Ocean) accompanied the railroad tracks most times, and helped businesses to integrate their operations and to maintain stores and factories in multiple towns--infant corporations, as it were.
The South - The railroad and telegraph had an influence here too, but to a lesser degree. Cotton production and slavery were more important factors in this time frame, as the South became the world's largest supplier of cotton, especially for export to Britain. This would heavily enrich only a few, however, and for the most part, daily economic life in the South was unchanged in this time period, remaining rural, agricultural and poor.
The Frontier West - The Railroad and telegraph win out here as well as the most important factors in my mind. Both of these advancements, and the industrialization that accompanied them, made it easier to migrate to and to live in the West. Travel was safer, easier and more convenient, and the tools, materials and finished goods that made life there more possible and profitable were available for order through the telegraph, and delivery through the railroad.