You're headed the right way.
IF you have video coming out of a card with its own output sockets on the back, rather than from a system on the mobo with an output on the rear panel of the mobo, then here's what is happening. There has never been any standard way for a sound chip on a mobo to send its signals to a video card. These days most video cards are sending their signals out on HDMI or similar, which DOES have a set of wires for audio, too. So how to get the audio to that video card and sent out on HDMI to the monitor? Almost all such cards now have their own audio chip on the video card to do that job. At the time that the card is first installed, the process installs drivers for both the video system and the audio system on that video card, and then configures Windows to use those devices.
This means your computer actually has two possible audio output devices. Now, Windows can only use one of those at a time, although you can change it easily. Likely Windows now is set to send audio out using the chip on the video card, so it is on the HDMI cable and going to your Monitor. It is NOT sending out any sound form the speaker jacks on your mobo's rear panel. If that is the case, then you need to check two things on the Monitor via its menus. First, ensure that it is set to accept audio input as part of the signals on the HDMI cable. Then ensure its volume control it turned up.
YOU can change where sound comes out of your system when you wish with a Windows configuration setting. At lower left type into the search window: sound settings, and it will pop up a window for that. In the drop-down selector window at top look for an audio output system named like your video card. IF you choose that, sound will come out of that card to your monitor. OR, if you choose the mobo system (likely Realtek), sound will come out of the jacks on the mobo rear panel where you can plug in speakers.