The fact that now you DO get audio at your monitor's speakers when using an HDMI connection cable tell us that sound may be generated by a DIFFERENT audio chip. So question: is your video feed to the monitor from a video system in the mobo with an output socket on the back I/O panel, OR is it fed from a separate video card plugged into a PCI slot with its own HDMI socket on its back plate? My guess is that you do have a separate video card you are using.
It is very difficult to feed sound from a mobo audio chip system to the HDMI output socket of a separate video card. For that reason, IF you are trying to use a video card plus a mobo audio system, normally you would use a DVI cable from video card to monitor which gets you no sound at the monitor, and then you use a separate speaker system plugged into the audio output jacks in the rear I/O panel. That's my set-up with a 5.1 Surround Sound speaker system and earphones in the front jack. That sounds like what you had working before., but not now. Because many people using a video card want to feed both video and audio to a monitor from the HDMI socket, video card makers have a different way to get sound to that cable. The add a new audio chip to the video card so they can send sound out on the HDMI cable. From Windows' perspective, this is a second and different audio output device in the system.
Now, Windows can use only ONE audio output device at a time, no matter how many devices your system has. Right now it is obvious that it is set to use the audio output system associated with your video output system. If I am right and that is a separate video card (NOT a mobo-based video output), then the audio output chip on your MOBO, which feeds the rear panel jacks and the front panel jacks, is NOT being used by Windows. So, even if that mobo-based hardware is NOT damaged, it will not send out any sound signals to use.
You can test all this. Go though Control Panel and the Sounds and Audio systems panel to the Audio configuration tab. There should be three separate boxes that each allow you to specify the Default device that Windows will use three types of things: Playback, Recording, and MIDI Playback. I bet the Default Sound Playback device is set to the audio system on your video card, and NOT to the system on your mobo (which is likely by Realtek). You can change that and then back out. Now try your sound tests, after connecting speakers or whatever to those rear jacks you used before. If the mobo sound system still works, you'll get sound that way. Now test whether the front headphone jack also gives you sound. If it does, all your system is OK.