It shouldn't matter if the audio is from a sound card or not.
What is the brand and model of TV? I can likely look at its manual online and discover how it handles/routes audio.
Some TVs have one particular HDMI input that is designed for this kind of use, and will switch to using the 3.5mm jack for audio on that particular HDMI input if it senses a signal there (or it may be selected in a setup menu).
An alternative may be looking for DVI or VGA input on the set and connecting the computer there (along with an associated audio jack) -- unless you are trying to play Blu-Ray discs on the computer, in which case HDCP (High Definition Content Protection) may prevent the VGA connection from getting HDCP content from the Blu-Ray disc.
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OK, I found the manual for AOC model L32H961 online, and I am going to assume that the other models in this family (L32H[n]61 series) are similar.
The 3.5mm jack is associated only with the VGA (PC) input.
The RCA audio inputs are associated only with their respective component and composite/S video inputs (indicated by a box drawn around the connectors in common).
The HDMI input can use a DVI-to-HDMI adapter for devices that have DVI out, but this set does NOT associate any analog audio input with it (the manual states "Note: The DVI to HDMI connection provides video only. Connection to an alternate audio player is required for audio"). So you if you are using the set's HDMI input you will get no audio unless carried on the HDMI.
Looking up your graphics card, I find it has two DVI connectors and no VGA connector. BUT (at least the PNY version I found) IT COMES WITH A DVI TO VGA ADAPTER for use on one of the DVI outputs! So, hook that up to the TV's VGA connector and its associated 3.5mm audio in. That solves everything but the HDCP issue on Blu-Ray discs played through the PC (but note that VGA connectors are quite capable of 1080i/p, it would only be the HD content protection getting in the way). That would be the cheapest way of fixing this (all you need is a VGA cable).
More expensive would be a DVI plus analog audio to HDMI (carrying digital audio) adapter box. That would eliminate the HDCP issue, because DVI can handle HDCP (VGA can't, because it's actually a form of analog component video).