If it is white noise, it's probably the floor noise level of the sound board output. Check the Signal/Noise ratio (SNR) of the sound card (or on-board sound) - if it's less than about 86db, you will notice some white noise.
Try to mute Line-In, CD-Audio and everything on the windows mixer except wave-out. A lot of times white noise comes through the line-in input.
If you get squeaking sounds when there is hard-drive activity and stuff, it probably is interference in the sound card from within the computer. In that case, try another sound card...
But I don't know why you get white noise with the computer off... Isn't it the alternator whine (varies with RPM)? If so, the cause may be ground loop, you can try to isolate the ground wire (shield) from the RCA cables on one side (either at the computer or at the amp side) to see if the noise lowers. You can try also to use better quality rca cables with better shields.
Anyway, if you are willing to spend a little, get an USB sound "card" and an USB extension cable and put the sound card right next to the amp - that should solve all of the above problems and give you the best quality sound.