DVI=HDMI without sound. a connector like this would solve your video problem immediately:
you can also buy full length cords that are dvi on one side and hdmi on the other. this wont fix give you audio.
i would definitely NOT want to send audio thru a pc unless you already have the input hardware. you will have to set the audio up on the pc every time you want to play. the easiest solution (if not elegant) is to buy a 2nd set of pc speakers or a headset. you could buy audio input hardware for the pc and enable it whenever you want to play a game.
you are going to send video thru hdmi and audio thru the av multiport. this is how older hdtvs with dvi and no hdmi use ps3.
im guess you wanted a solution using the component part of the av multiport. the problem with your monitor input types are that analog rgb and digital are just the types of signals it can accept. component video uses YPbPr and isnt compatible with rgb vga without a really expensive convertor.
how is your monitor connected now? i assume vga? does your pc have dvi or hdmi out?
if you asked me to do this here is the fantastical diagram i would draw. pfidc and admin will like it.
-one hdmi switch (must support hdcp)
-one hdmi to dvi (from switch to monitor)
-one dvi to hdmi (from pc dvi out to switch hdmi in. if your pc has hdmi out use that. or displayport to hdmi)
-one hdmi (from ps3 to switch)
-one av multiport (from ps3 to speakers)