If I didn't build it, I don't trust it. Been building PCs since... 1994? First one was a 386DX2 40 in an old AT server case.
In my experience, pre-built systems are overpriced and underpowered, usually with a great processor, slow RAM (but plenty of it!), shitty factory-underclocked GPU, and slow HDD (with just enough storage space to look impressive!)... for about twice the price of its component parts... three times if its an Apple product.
My current rig is dated, but it works well enough for now. Built it in 2007 and have only added HDDs since (through a mashup of different hard drives, it has around 3.2TB of storage space now). I plan to keep it running as a file server when I do get around to building a better system... which won't be until I either cave and decide Windows 7 isn't as terrible as my experiences with it have been thus far, or I start getting the option for Linux-native gaming in every game I want to play.
*edit* oh right, how did the build go... no issues. Haven't made a mistake in a build since before I was legally an adult. Also, the case didn't require any metalworking, so that was nice.
As for the semantic difference between building and assembling a computer... you can assemble a motherboard, but did you etch all of that silicon by hand? Those ICs aren't your work. I suppose there's no such thing as a computer any one person "built".