@above, the person wants to use the ports on the front of their case for audio, not the monitor or tv. whether the dvi cable or not handles audio is mostly irrelevant.
second, dvi-d is more than capable of handling an audio signal in a hdmi-dvi cable. only the older iterations were incapable of audio for the record. i've been using dvi-d for audio applications the last 10 years so can verify that it is indeed a thing.
@op
if i understand you correctly:
A) with the pc plugged into the tv via hdmi you get audio on the tv ( or audio on your front jacks when you plug them into the front jacks)
B) you get audio on the front jacks when you do not have your monitor plugged into your pc
C) the only scenario where you do not get audio is if you plug your monitor in via hdmi to dvi
are the above correct?
you may want to list if you are using a usb headset or analog.
do the rear jacks work in the above scenarios as well?
the first thing i would try is in playback audio devices right click and show disabled or disconnected devices. does your headset show up there? if you are still having issues i would remove your audio and video drivers then reinstall the lastest versions as you could have a version with a compatibility bug or similar issue. for video card drivers i would suggest using DDU to be sure its gone. please download the newest version to your pc before uninstalling as it will make things easier.