I went to the hardware store pulled a bunch of LED bulbs off the shelf. One of the bulbs found its way into the wrong box and had a significantly smaller screw base than your typical light bulb base. Because I wasn't paying attention to this as I was putting in all the bulbs, I inadvertently attempted to put in the bulb with the smaller base which tripped a breaker, causing all my power to go out. I switched all the breakers back on and my power came back, but now my light won't work. Did I destroy the fixture forever or is there something that I am missing here? It's wired up to a dimmer control if that is of any use here.
TL;DR: The dimmer's toast. Replace it.
The short circuit or overload condition indeed likely smoked the switching element in the dimmer; modern dimmers use a special type of transistor-like switching element known as a triac to cut part of each half-cycle of the AC wave out in order to reduce the power being applied to the lamp. Unfortunately, triacs are very intolerant of short-circuits, and to make a short-circuit resistant dimmer would drive the dimmer makers out of business, so dimmers just let out the magic smoke whenever shorted (such as when a portable lamp is on a dimmer, and the bulb is broken).