I would see if you can't find similar but cheaper parts to trim off some of the fat on the custom built machine to make him feel more at ease. I just built a system for my friend minus keyboard, mouse, OS, and monitor for less than $500. Considering how cheap you can get a mouse, keyboard and monitors these days....you could likely get him built for $650 and still have better quality than the Emachines.
I would point out to him that if he wants to game, he's going to need a seperate video card anyway, and onboard video really doesn't get the job done...not to mention the fact that it sucks away system resources.
Sounds similar to a friend of mine trying to sell his Harley. The guy wants it, has the money, the wife likes it, but is afraid of Harley's after getting a ride on a larger bike ( crotch rocket ) and a driver that...well, isn't the best person to give a good first impression. She knows her husband can ride it, but she's afraid to be a passenger. How do you convince her that just because it is a bigger bike, it isn't more dangerous?
This is just an example folks, lets not get off topic and start talking motorcycles here