"I'd need to run a cable of at least 35 feet."

Another idea rather than cables is to setup a small FM audio transmitter next to the player, and an FM receiver next to the computer, and then run the sound into the PC.

There some technical problems that need to be addressed, but if you have a reasonable quality FM stereo that you can use, you can get small FM short range transmitters easily now (often used to hook up iPods etc to to car stereos etc), you used to have build up kits a while ago.