I totally agree with your points 1 and 4. Ofcourse your processor can calculate sound, but it's the AC that is important. When I plug in my headphones in my onboard soundcard and move my mouse I'm hearing noise and hiss. When I play music I can hardly hear it, but it's there and you will notice it when the music is soft.
Need great sound: get the digital signal out of your PC and have an AC outside your hardware.
1) On-board sound isn't very good, in my experience. Admittedly, my 2006 Macbook sounds considerably better than my 2010 Toshiba.
2) My favorite headphones are the Etymotic ER-4P. I found mine online for a bit under $200. They're an almost perfect aural match for my beloved NHT 2.5i speakers.
3) The Boostaroo is a horrible amp. Unbelievable hiss and distortion. I don't know how they're still in business. If you need a portable amp, look for a CMOY in an Altoids tin, off eBay. Cheap and (IMO) vastly superior.
4) A computer's case is about the worst environment I can think of for audio electronics. Get any sound card which gives a digital out, and feed that into any consumer-grade receiver that supports digital decoding, like a Pioneer from Costco. This way, your uncorrupted digital stream gets converted to analog well away from the noisy PC case. You'll be 90% of the way to a ultra-high dollar sound for a couple hundred bucks.