By run for I meant how long it will be turned on with out being shutdown.
As for sound this does matter with headphones. Trust me, the computer next to me can be heard though walls and doers to the other side of the apartment. If sound really does not matter getting it to 4.0 is easy as all you do is buy the biggest baddest fans you can afford and a decent heat sink.
That should get you to 4.0 easily all within your budget. It should also come out quieter than my current system as you are only going to use two loud fans. But yea, that will cool it easily... all within budget!
(Note that you can find most of these parts for less at other stores, prices here are maximum)
yay for arctic 5. I keep an extra one of those lying around at all times