That remote wire is probably grounded through the FM antenna. That would cause enough EFI in the antenna to screw up any FM reception.
Although that wouldn't explain how you lose FM reception when you use the "stock remote wire"... What is that, exactly?
You say you have the PC audio going through the headunit, you don't specify how the audio signal from PC gets to the headunit. AUX input? FM modulator? Cassette adapter?
Also, where is your antenna and what type is it? Could you have an antenna embedded in the window/defroster by any chance?