Standard DVI does not carry audio at all, so don't waste your time trying - it's not a limitation of the BC6, but the connection itself.
As I understand, the settings in the BC6 allow you to get video input from either the DVI or component (YPbPr) connector, but audio needs to come from somewhere else. This is where you need the AV sockets.
There is probably some logical explanation for the component input not working for you, but I suggest you leave that be, as the DVI connection will give you a better quality picture anyway. I suppose all you need now is to use your DVI cable, then connect the PS3 audio with RCA cables to the AV3 audio connectors and configure it correspondingly in the connections menu. Should be possible to use a digital audio connection as well, but it will again need to be in addition to the DVI cable.
EDIT: I consulted the BC6-26 setup manual, and I believe your best & simplest bet is to connect with DVI and analogue audio from PS3 to AV3 L+R; then assign AV3 as "PC" in the connections menu. Digital audio apparently requires that you have the surround sound option installed in the BC.