Sounds like you're just justifying your purchase. Yes, it might be a nice PC but not worth the money. I have a mITX case with Intel's standard cooling which isn't great at all but it rarely gets noisy when backtesting. In any case, a passive cooling solution for your CPU is less than $100. GPU fans nowadays are silent in trading usage and there really aren't any other noise factors I can think of - even fairly cheap PSUs produce very very little noise, almost completely silent...the wind outside your window probably makes more noise.
In my experience, the $110.00 Fractal Design R5 stays absolutely silent with a top-end Noctua cooler while running only SSD's (although some hard drives such as the WD green's are a pretty quiet addition, albeit noticeable). I have an R5 enclosing a delidded, 4.6ghz overclocked 6700k and it stays icy cool -- cooler than any other machine I own (although not rock-solid at the voltages required to get it there). In contrast, my 7 other machines, including the laptops, are each noticeably loud from the next room when they're running 2 or more cores full blast.
I use the Fractal Design R5 too. Quietest case I've ever used even with 5 fans and a water cooling pump. Multiple SSDs and WD greens as well. Highly recommend this case
Tigerdirect.com. just built a supersystem with all the bells and more capacity than yours. Paid less than half the asking. Plug and play components takes about 30 minutes to assemble. Why did you pay retail? Did your friend do what I did? If no, then why not?