I have an idea... thought not i'm not 100%
The reason your not getting sound is because the HDMI is a digital signal and the coax is analog... and i don't think the digital and analog audio is bridged in the tv if that makes sense...
Basically, from what I understand if your inputing a digital signal into a TV and the tv has analog outputs you it won't output the digital signal via the analog outputs as there is bridge in the TV between the digital and analog systems (I think)
Anyway... also this thread might help abit.... I skimmed over it and it seems to be related to your issue...
Ps3 outputs? - PS3Forums