is it worth it to learn how to build my own computer and snap together the parts, or should I just buy a computer?

Only if you're a real man.

To tell the truth, the main reason I'm still running on obsolete hardware is that I don't have time to upgrade and I can't bring myself to just buy a whole new system. I've been replacing things a part at a time since, um, 1989. I've gone through like 12 computers in that time, but never bought a whole one.