The key to this puzzle is that the LED billboard represents Conway’s Game of Life, which must be played one generation or “tick” forward in time. Live cells are indicated in yellow, and dead in gray (the color scheme was chosen to match this simulator, which should be one of the top Google results). Canonically, Game of Life is played on an unbounded grid, which is the case here. Because there are simulators that can run it on different topologies, the fact that this is “one still-functioning section of a large LED billboard” is meant to resolve any ambiguities.

The grid as given to the solver initially is incomplete. Solvers may notice that all answers are made of 1–3 trigrams that fit the pattern Consonant, Vowel, Letter. The 21 circles atop the rows and 5 to the left of the columns correspond to the 21 consonants and 5 vowels of the alphabet. So any consonant, vowel pair can be interpreted as an x,y coordinate. The key insight for the third letter is that the “blackout” has necessitated the use of Braille. Solvers can then input the third letter of each trigram as a Braille letter, with the upper left dot of the letter placed in the cell given by the x,y coordinates. Raised dots in Braille correspond to live/lit cells. So as example, PIE would be the Braille letter E, placed with its upper left live cell at the intersection of column P and row I, and another live cell at (Q,O). This approach to placement is confirmed by the overflow column and rows in the grid, as well as the fact that live cells never crash into each other (whether the pre-placed cells, or those from two different Braille letters).

The completed grid is below. Lettered cells correspond to live cells produced by the raised portions of Braille letters.

Once all Braille letters have been placed, running the Game of Life forward one tick produces a new grid where the center three rows consist of 11 Braille letters, offset from the top and bottom by dead cells. They can be decoded to read DECAMP TO LEX, which is the instruction you give to the Continental Army to save their New Year’s Eve party.