It sounds like you have a ground wire problem. You must make sure your stereo is grounded properly. If not, you'll get humming, noise when the lights, wipers, etc. go on. Find another ground for your radio and see what happens.
Crew is right and another thing to consider is that you don't want to extend any ground wires. It will only allow more noise problems! Keep your grounds as short as possible, as large of a diameter wire as possible (within reason for the load) and be sure it has good metal contact to the vehicle chassis.
Often, with high current demands for amps, I'll drill and clean 5/16" hole in the body for the ground then use a bolt and nut going thru the body to assure a long lasting and trouble-free connection. As stated, do check ALL connections including molexes, line level RCA's and grounds.