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.