A problem with line-in hum
Your body and the cable act as a (poor) antenna that helps get more of the 60hz EMI into the line in amplifier. Assuming you're using the stock line in on the PC, the line in circuitry isn't very good and doesn't have as much 60hz rejection as a higher end system would. Unfortunately, 60hz is all around and usually a great deal of effort is put into the design of studios and studio equipment to minimize it. For more consumer oriented products, perhaps a higher quality sound card would provide better results.