Knowing the insides of computers as I do, I must comment on this. The only difference I have ever seen with different power cords is in the sounds that fans, 15,000rpm hard drives, and some differences in the sounds that eminate from the power supplies. As far as burning digital information, I am guessing that most of this is coming from mp3's, which are uncompressable data, It is literally impossible for a power cable to make a difference in the sound coming from changing parts.
Lets say that "cleaner" power can make a difference on your zeros and ones, but you must think about what the power must go through before it gets to the CD burner, first it goes through the power supply and get tranformed from 110vac to 12vdc,5vdc,-12vdc, and -5vdc (where the cd burner is concerned, there are actually about 8 or 10 voltages that the motherboard requires.)Now out of the power supply we have four 22G(?) wires (red, black, black, yellow) that deliver the power to the cd burner. Once inside the cd burner the power goes through traces on a circuit board to a connector for the drive motor which which runs off of 36+ gauge wire. On the laser end you have everything runnung off of a small ribbon cable, probably more like 40+ gauge wire. So tell me were in this chain can a bigger power cable effect your cd burner?
Please keep in mind that the above statement is ignoring the fact that ones and zeros are not effected no matter what you do to your system. Like I said MP3s are uncompressable, and CD's are still digital, so the conversion to analog happens in your sound card/cd player.