Update on my Audio Issue
Well, seems like HP, with this laptop anyway, muted the headset by default. Of course, with the headset plugged in and muted I couldn't unmute it without someone to look at the screen while the headset was plugged in.
Once I got that done, I discovered that it was muted, unmuted it and all is working great now. What a silly thing for HP to do, mute a headset by default.
Thanks to those who responded to my problem