I'm not sure I'm supposed to give my entire train of thought as to how I reached my guesses, but I'm going to do that anyway.
So my guess for the number lock is a total stab in the dark: we need four digits and no number combinations are apparent, so I'm going to take this literally: the text contains three written-out numbers - two, seven and eleven - which combined makes
2711 my best guess.
As for the digital display, when turning the italics and bold letters into dots and dashes for morse code - the flickering light hint definitely helped -, I get "AZURE CYAN LIME INDIGO". I'm not sure what to do with these colour names to get a 9 letter code. Lots of 7- or 8-letter words but no 9-letter words come to mind. However, it may not necessarily be a word, so what I CAN think of is using the 9 colours of the rainbow/light spectrum and turning those into a letter code, which gives:
Infrared-Red-Orange-Yellow-Green-Blue-Indigo-Violet-Ultraviolet =
IROYGBIVU
I hesitantly enter 2711 on the number lock and use the stylus on the pad to write IROYGBIVU.