Correct.
I see now - so you physically broke the audio port in your computer, yet it's "the technology" responsible for distortion. Gottcha.
Sarcasms aside, in your particular case using other means other than broken analog port to get sound out of that computer are probably beneficial.
All this convo is absolutely has bearing what so ever to original OP's question - is HDMI is best way to connect HIS PC to HIS Yamaha receiver and the answer is simple YES. HDMI allows best possible digital signal to be passed to excellent audio processors inside OP's yamaha receiver.
While you could use external dacs, software processing, any other wizards and gadgets - the simply truth is $200 spent on speakers/sub would be much more beneficial than spend on gadgets etc...
I mentioned way back the 3.5 was useless/unservicable...not the tech. But any on-board DAC can bettered by a quality external DAC.
As to the original post, I said adding RC would be a benefit to the HDMI out. No room is perfect.
Most certainly, the speakers are the most important part of a system.
But your economics are off. In today's dollar, $200 spent on a pair of speakers, or even $200/ea is not providing much in upgraded sound.
Its been 40 years, give or take, since I auditioned a pair of speakers at $200/ea I thought were worth buying.
Today, its more like $500~700/ea, minimum, to get something worth keeping.
The XOs I built 12 years ago cost almost that much alone.
But no matter what speakers are being used, Dirac RC can improve the sound.