Many people here recommend the use of an external DAC. This can be achieved if you have a digital out on your sound card (many have this), or via a USB-attached DAC. I will leave it to others who have done it to comment further.
1/8" jacks are a pain ... if your lucky it's the cable. I'd spring for a new sound card with SPDIF out. Most even have optical digital out now and a cheap DAC if your receiver doesnt have digital in. I did it and it worked really well. If the hum is REALLY bad and you dont experience it with powered speakers hooked to your PC ... try a diffrent input on the receiver - ground evrything together and tie it to the gounding post on the receiver. Try a new cable. Make sure your connections on the sound card side are correct (dont plug into the mic-in). Lightly wiggle the cable and see if the hum changes or goes away - your connector on the sound card might be toast if it does.
That is everything I can think of ... good luck
PC's emit a good amount of both EMI and RFI. Between the power supply, CPU, and bus I don't know how you could shield the soundcard and most importantly the DAC chips on it. Special care would have to be taken not to short anything out. You might try using ERS cloth over the whole soundcard or just some bluetak or two sided sticky jell on the DAC chips and putting a small piece of copper shielding on top of that. Probably should ground the shielding to the PC chassis.
But the best and easiest thing to do is just use an external DAC.