If your display has a HDMI connection you STILL need to make sure that it will be compatible with a resolution which the PS3 outputs. If your monitor is not compatible, then you won't get video. You will have to carefully read your owner's manual to see if this will work.
Likewise, with your audio card, you likely can't do it unless it has audio INPUTS which isn't always the case, especially with digital audio.
The PS3 is designed to connect to your TV, not your PC, so you will need to include some specific details of your make/model for monitor, audio card, etc. if you want specific detailed help. Even then, you may not like the answers.
I would just get a 19" TV - or a 100" projection setup.