The reason you can hear less noise is because the vid card is further away from the MB outputs. So this means that the current or EMF is going across or near the backplate of the MB. To try to fix this put a good shielded copper wire from the screw holding in the video card to a screw on the PSU. Then all the junk noise should preference this to the PC case.
You definitely want to use the 16x slot, as the other one will suck, so try and fix it.
(separate problem), but... If the receiver died then the OHMS/resistance of the speakers might be too low which puts stress on the receiver (all the extra current).
Make sure the low frequencies are not too much for the speakers... to do this you need to set the correct speaker setting in windows. If you tell windows you have surround with subwoofer and speakers are not really up to it then it might take a bit of tweaking.
It is not really truly grounding but the EMF from video cards that causes problems. To reduce problems you need to check everything is using the same power-point and reduce feedback loops.
For the speakers reduce the volume on the speakers and increase the volume from windows, might get rid of the hum for the same volume.
Try with headphones and switch between headphones and other speaker settings in windows and you will see what I mean... it is because the sound from the MB is good quality and the frequencies stress low ohm speakers, not the opposite... if the MB was poor quality you would not hear distortion as it would not bother with the low frqs.
Also (again not really related to your noise, but I always crap on) I don't know what the speakers are, but assuming it is a media server. If they are decent Yamaha or something then buy some proper connectors for the speaker wires where they go into the speakers (i.e. don't use bare wires. If they are not banana.. use speaker pins like these
http://www.selbyacoustics.com.au/StoreFrontProfiles/deluxeSFshop.aspx?sid=1&sfid=74520&c=84100 These bent looking pins hang from the back of speakers that normally clamp wires, and although they seem weird and crappy actually make a good connection which avoids the crackle of wires moving... not your problem, I know, but good to know.
If you can't fix it then try a friends video card to see if that is the problem. Else blame the board or the speakers I suppose, short speak wires might help.. or just moving them. The PSU might also be causing the problem, but probably not likely.
Also, what case do you have?
One that is all steel with the PSU on the bottom (or left for desktop/media case) will give the best sound because then the earth does not pass near the backplate. Also make sure you used all screws, no connections are bypassing the rubber backing on the backplate and the vid card is screwed in. The CPU heatsink might also be creating an earth loop... google "earth loop".
http://en.wikipedia.org/wiki/Ground_loop_%28electricity%29
