Hi, Welcome to LQ!
To get fast sound from a pc, you'll have to get a dedicated sound card.
There will be a latency with OnBoard sound chips, that will be hard to overcome.
A cheap pci card will reduce the delay significantly, but there will still be a small delay.
A more expensive but profoundly better option is to get a firewire or usb solution,
where you can get very fast (low times) latency, (the time it takes to get a signal from the input to the output)
And being outside the box (pc) there's all of that electronic noise (rfi) from the pc the sound circuit won't have to deal with
requiring less cmr (common mode rejection ratio, for amplifier circuits) and less distortions just from the extra shielding.
There may be other ways but I haven't found them easy.
A better option would be to use the pc as the jukebox and get a mic preamp (small mixer) and use that to get the mic into the TV.
You may even be able to make one that would plug into the tv rca connectors.
With a small mixer, Plug the pc and the mic into the mixer and that into the TV. Most small mixers have mic preamp/s
I have a Behringer xenyx 802 mixer. Under $100 (au). 2 mic's, 2 stero lines, tape and fx-send and str aux returns too.
You've picked one of my favourite topics, This post is getting long.....
I hope this gives you some indications.