one of the good things about a formal CS education (well, mine anyhow) is that they force you to do things like write in assembly. obviously there's far less immediate practical application these days, but the exercise is definitely valuable, and probably not something I would have done voluntarily. Actually, it feels like something I would have thought sounded cool, tried, and then given up on when it got annoying.
You can make transistors with some...hazardous components, but you may want to start with relays or tubes and resistors (which could, theoretically, just be varying lengths/guages of wire) and build NAND gates. It would be big, hot, noisy, slow, and a huge waste of your time, but there were computers before semiconductors.
Relays are doable from scratch (mining and refining copper; winding coils, etc etc) but it's going to be pretty hard work and you're going to have a very slow computer at the end of it.
