Regardless of what mentioned above, I have some add ons for the role of computer in headfi system.

Computer are just like CD transporter or music player that can provide digital signal. So it does affect the sound quality of the DAC. Connecting to different computers, it's quite normal to hear different sound. @xEDynamics also told me that the sound of Aune T1 is different on my laptop and his laptop/pc.
That's why some passionate pc-hifi users intend to build a "HTPC" (Home Theater Personal Computer) or "CAS"(computer as source) system.

You can read some articles from "Cplay" and "Jplay" forum. They use different method to optimize computer hardware and software to get a higher quality sound signal. Even sata cable, hard disk, PSU, fanless radiator, computer casing...will influece the sound quality.

They also develop software to get a better sq. You can try J-play, especially "hibernate mode". The background of music is very dark and quiet, and the outline of music is more solid. (Note Trial version is fully-functional apart from occasional inserted silence)
http://cicsmemoryplayer.com/index.php?n=CPlay.Download
http://jplay.eu/download/

Now pc-hifi mainly seperate into two. One of the groups goes for high performance hardware to maximize the potential of the computer as a music player.

Another group goes for low-power consumption hardware. They thought that a high quality fanless PSU which can provide clean and stable electric power is necessary, but just for music playing doesn't really need high performance cpu. This is because high performance CPU might need more power consumption and might poluted the sound quality. High performance CPU also cause more vibration and affect the stability.

Actually I'm not too familiar with "HTPC/CAS", just sharing some experience. But I'm quite sure that different hardware will made the sound difference.
I've tried a HTPC which was build by my taiwan friend, the sound quality is really amazing, sound like a high end cd transporter. Although just using USB output, compared with my friend's HTPC, my laptop really sounds sucks.