Hum in speakers when I plug in to computer

Speaker hum is usually due to (1) RF interference along the cable, or (2) something called ground loop.

(1) can be addressed by using a shielded cable, RF chokes (the magnets you see at the ends of some cables), or using unshielded twisted pair instead of RCA (a proper adapter will break the audio signal into two duplicates, invert one, and send both over the UTP cable; any interference will cancel out when one signal is inverted and the two are added together again).

(2) is tricker. It's caused by the electrical ground on one piece of equipment being at a slightly different voltage than at other equipment. This causes something like a DC current between your equipment, which your speakers interpret as a hum. The quick and dirty fix is to use a long extension cord (with a 3-prong plug for ground) so your speaker system and computer are plugged into the same wall outlet.

The fact that you're not getting the hum with your phone (it is electrically isolated from your home) suggests that (2) is the culprit. As a quick and dirty test, haul the computer over next to your amplifier and speaker system. Plug it into the same outlet (use a power strip if you have to - all that matters is that the equipment shares the same ground). Use the same cables and see if it takes care of the hum. If it does, you can just buy a 20 ft extension cord to go with your 20 ft RCA cable. Though that may necessitate you switch to a shielded RCA cable (the unshielded cable is basically a 20 ft antenna which will pick up the 60 Hz AC traveling over your new 20 ft extension cord).