Q: "Build a PC", "assemble a PC", or something else? When you have all the parts of a PC and you need to connect them into a working PC, which is the appropriate verb to describe this action: build, assemble or something else?  

A: To me building a PC is buying all the actual components (RAM, SSD, sound card, screen, etc) and putting them all into a case to make a computer. Whereas, assembling a PC just sounds like unpacking one from the box and plugging everything into the right port.

A: You assemble a kit into a PC; you build a PC of choice configuration from the parts as needed.  
So, decide if you want it a la mode or a la carte.  

A: When "building" a PC, you're just assembling a pre-produced, unique, specialized and working parts into a working rig. The most logical word choice here is "assemble".
Building would imply making those working parts from scratch, but that's what factories do.

A: Assemble is the verb you need to use, as you are putting together all the parts.
All PC companies, and even the ones who custom-make them, use the word assemble.It is the accepted industry term.                  
Assemble:
fit together the separate component parts of (a machine or other object).
"my new machine is being assembled and my old one dismantled"
(Google dictionary)
