How to troubleshoot static noise in headphones connected to a computer that persists even after replacing the sound card

It can be a few things, depending on exactly the type of sound.

1. Coil (possibly also capacitators) whine These are known to sometimes resonate under specific currents. It's a defect for sure. And the laptop can (should) be returned for the problem to be fixed. Here's an example of type of noise (starts at 00:20 mark): http://www.youtube.com/watch?v=SeahtqeTrGo

How to know if this is the problem? Because the noise is actually dependent on current draw, the noise should vary in intensity and even go away (and come back on) when forcing the computer between idle and load conditions. Loading games that ask the graphics card to draw more current (and consequently the PSU), should, if this is the problem, alter the intensity, remove or generate the noise.

Another, more extreme example: http://www.youtube.com/watch?v=f-qdWVk5wzs&feature=player_embedded

2. Bad grounding This one is common if your electric connection or the device (computer itself or power adapter) aren't properly grounded. Here's an example of the type of noise: http://www.youtube.com/watch?v=yfmMlCfyxxc (starts at the 1:40 mark)

This noise affects speakers, internal or external, but only if you are sure this isn't a problem originated by your own electrical installation. Trying the laptop on some place where you know grounding is properly installed is a sure way to know about this. But if this is caused by your electrical installation and you have no way of fixing it, you can acquire a ground loop isolator. These sell at peanut prices: http://www.google.com/search?q=ground+loop+isolator

Here's another, more typical, example (starts at the 00:30 mark): http://www.youtube.com/watch?v=CvMHmgFjf_U

This is a classic, if extreme, example of why some audiophiles really prefer discrete sound cards rather than onboard audio.

What is happening is that there is no isolation (or the isolation has failed) between the signal pathways for data and the signal pathways for audio on your mainboard.

When electricity, even miniscule amounts, runs along one pathway and runs parallel to another pathway, sympathetic electrical currents will be created in that parallel pathway. Audio equipment is especially susceptible to this because it eventually converts any digital information into analog, and those random bits of sympathetic current suddenly become audible sounds.

This principle of sympathetic currents is the same thing that works inside a transformer, where coils of wire wound around ferrite cores create magnetic fields which excite electrons within coil of wire around a core which are parallel to the original. The ratio of the number of coils in each wire and the composition of the ferrite (iron) cores allow for control of the output current based on the input current.

If you're just curious, this is the answer.

If you want a solution: More expensive mainboards generally have some sort of correction or isolation structure that prevents most of this cross-talk. Or a $10 soundcard from your local electronics store, simply because it processes the audio signals in a local physically distant (even if only by a few cm) from the electronic noise on the mainboard, will produce a markedly quieter (not quiet, but less noisy) audio signal.