PC Speakers make a crackling buzzing static noise while computer is running certain processes.

In addition to the issues noted above, this may be a bad grounding issue. In either case, the exact cause may be difficult to isolate, much less remedy, outside of a tech's shop. Even in a controlled environment it may be cheaper to replace than fix.

If you try a different set of speakers, be sure to avoid using any expensive components.

If possible, identify a minimal set of actions that you can perform to replicate the issue. Can you make the PC do this at will, or is the behavior separate from your actions. What else is going on at the same time?

Keep in mind factors external to the PC - is there a printer, shredder, fan, or lamp plugged into the same circuit? Do the lights in your house dim or flicker at the same time?

Hi sbriffe,
in addition to the both comments,,,
the problem is your wireless receiver/transmitter,as Callandor you must put the speakers  min 1,5 m~3m away from your wireless net card/router,but i doubt it will 100% help,,,just the same effect you can see if you put your gsm/handy just infront of your speakers ( ,but you know frequences from belkin card-to linksys router and  gsm frequences are different ,don't expect 100% the same reaction of your speakers ) ,,, there are also other effects which may be specified as influence of non shielded speakers to other devices:
http://forum.ecoustics.com/bbs/messages/1/13228.html,,,,but this is not your problem ,,,
i don't think you can shield your speakers against wireless frequencies in case of router-wireless nic-connection ,but as Callandor buy shielded cables, and thus you can extend the distance between speakers and soundcard plugs, put both of the speakers quite away from the active range of the belkin wireless nic card/linksys router,,,the speaker's position must not cross the straight linksys-to-belkin line of connectivity,,,
cu

The wireless connection may be a factor, but on the other hand, the RF connection is live at all times, so there is no real explanation to why the noise appears randomly. If the noise could be coupled to network activity (downloading mail or something) it would be a cleaner case.

This can also be a power problem. Depending on your situation, there can be several causes of interference on the power mains (electrical machinery of different kinds) that can be really problematic. You could try with a simple surge protector in the power feed to your computer and speakers (if they're powered speakers).
/RID