LAPIII said:
Yes
Then bare in mind that this is all you should aim for , like you understand the tv is 11 years old , probably the hdmi standard was still crawling into scene and the tv identification chip most probably had the worst uncomprehensive EDID data reported to identify its capabilities .

So you can always try what @itsme1 said since he say he have had a similar tv , now if that still fail continue reading this .

I believe there are 3 phases to go through , first one is to make sure you have a decent hdmi version 1.4 cable , if still the gpu fail to recognize the tv as audio capable device then head to phase two and research creating a custom driver INF for your tv over-riding its original EDID data to one that states it is an audio capable device , and to be honest i was never successful in that to give aid here , then final phase , to embrace the fact that this is as far as that old tech can buy you and settle for it as an extended display along with your pc speaker output just with less feel of guilt .