Right now, the LED just runs randomly through the cases, and the Serial Monitor shows random numbers (in the range specified) being generated. So, the code I copied seems to be working as it should, just my edits in regards to the switch are not doing anything 
ardly - I thought my problem was exactly what you described - when the switch is up, the code produces a random number, and generates the corresponding case, on loop.
What I'm confused about is that it keeps doing this even when the switch/button/tilt state is low - so it seems that the switch isn't registering at all, which doesn't make sense to me.
Here's a very amateur schematic and a link to a video of the setup.
RGB_schema.pdf (62.3 KB)