I'm trying to hook up a new subwoofer using the wiring in my house that was installed when the house was built. The cable for the sub is just a coaxial cable with no ends, so I need to stick an RCA ...

bad idea, RCA uses an impedance of 75 Ohms, which you fuck up when you splice the wire. I'd recommend using RG6 cabling for the video, and, if possible, S/PDIF for the audio, but in lieu of that I'd ...