The HDMI to DVI cable works with any device that has a HDMI output.
However PS3's component cable only works with PS3 and PS2.
Curious, why did you buy component cable to get audio? If you want Stereo RCA output, the standard AV cable that comes with PS3 is good enough for doing that.
My suggestion is to use HDMI-to-DVI cable for picture (which works on any standalone or PS3) and if you're getting a standalone, use multi-channel output for audio output (since optical cannot pass 5.1 channel PCM).
A Home Theater Enthusiast!