What sound do you have? An integrated (on the motherboard) sound such as RealTek, IDT, etc? or do you have an add on Sound card? You didn't include that with your PC specs.
You have the front panel headphone and mic jacks plugged in, but doublecheck the connection to make sure it's plugged in correctly. The HD connector from the front panel should be used.
Next, are you using the correct sound driver
? You need the sound driver from the Motherboard vendor, not a generic "HD Audio" that Windows will install.
Finally, can you plug something into the Line or Mic jacks on the rear of the PC and get it to work? You don't need audacity to check this, if you plug something in you should hear it in the PC speakers.
One other comment, I have a recording studio. A guitar signal, directly to a PC input, is too low for proper operation. A guitar output is at "instrument level" which is very low level. The PC needs something near "line level" for proper operation. If you are using a guitar amp, DO NOT connect the Speaker out to the PC or you can fry the audio, but you can use a "line level" output, "preamp out", "recording out" or a small mixer that will amplify the guitar signal to a useable level.