Did you ever look at the control panel sound properties "audio" tab?
Was everything set to use your on-board sound?
The fact that you installed a new sound card and it still doesn't work, leads me to believe that something is wrong in windows, either in the control panel setting for your audio, or possibly some sort of mixer settings.
When you test, you should be plugging headphones directly into the green line-out port each time to rule out any other possible interference.
Are you positive that your CPU or motherboard isn't being overclocked, even unintentionally? Sometimes, when a motherboard is overclocked, it raises the speed of the PCI bus, which will cause problems with onboard devices and/or add-in cards.
I would try going into your motherboard BIOS and resetting everything to default just to be sure.
Also, are you using the latest BIOS for your motherboard? Maybe there's a know problem with the version you're using.