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Your monitor does not have an HDMI connector, nor does it have audio out capabilities.
First of all, is the card you have to remove definitely the sound card? Picture of it removed please.
If so, since you're now out of a sound card you'll need to order one; just get something cheap @ newegg for $20 or so.
See, here's the deal: That video card has it's own sound hardware on it; so it's kinda two cards in one. With the right setup you can run audio through a DVI or HDMI cable, and then the audio can pass through either the onboard speakers on the monitor (or HDTV), or if the display has any audio out (my monitor for example has a headphone jack audio out on the back) then you can run audio out to PC multimedia speakers or a home theater receiver.