PC SPeaker Not Beeping but PC boots fine??

As Berton mentioned, the Speaker plug is one that must have the correct +/- orientation. Common error.
Try turning it 180 degrees and test.

A PC speaker has no polarity, it doesn't matter which way you plug it in. Piezo buzzer is the same deal as far as I know. I have one right here in front of me and there are no polarity markings on it. Both leads are that same length too. Your stereo speakers may have a + and - on them but that's just to get them in phase. Nothing bad happens if you reverse it. They still work.
Front panel LED's are polarized and won't work if you get them reversed. The switches aren't though.

Why you don't hear a beep, I don't know? Either the speaker is defective, or connected to the wrong pins. Off by one pin left or right maybe? Other than that check the various BIOS settings.

alphanumeric said:

A PC speaker has no polarity, it doesn't matter which way you plug it in.

I always believed that too Alpha. Until I got this new Asus board, which came without a speaker. I got a piezo out and plugged it in - nada. Figured, what the hey, turned it around and BEEP.

I recall I tried a "real" PC speaker in one of my modern boards and it did not work, but a piezo speaker did. I suspect that modern boards don't put out enough power to drive a "cloth and magnet" speaker.

A "cloth and magnet" speaker has no polarity. It's normally driver by an AC signal, not DC. The piezo is more suited to a DC (digital) signal. There are piezo buzzers, and piezo elements. Piezo elements can produce sound and be used as a transducer. The buzzer can't, it will only produce sound. I see that this one has a polarity indicator, https://www.adafruit.com/product/1536, but this one doesn't, https://www.adafruit.com/product/160. I have the second one here on my desk in front of me. If the ones with a polarity indicator have a DIOD inside that would explain why they don't work when plugged in backwards. I've been out of the loop for a while now so my electronics knowledge gets a bit rusty some times.

In the early days of PC's the motherboard would actually send an audio signal to the "PC speaker". It was a real speaker. Nowadays a lot of the time, all it sends is a beep, (pulse) via a digital signal (square wave). Piezo buzzers are smaller and cheaper than a regular speaker, so guess which one they use?

EDIT: Looking at the description for the one I have it says " Piezo buzzers are used for making beeps, tones and alerts. This one is petite but loud! Drive it with 3-30V peak-to-peak square wave. To use, connect one pin to ground (either one) and the other pin to a square wave out from a timer or microcontroller. For the loudest tones, stay around 4 KHz, but works quite well from 2KHz to 10KHz. For extra loudness, you can connect both pins to a microcontroller and swap which pin is high or low ('differential drive') for double the volume.

If what your plugging into the speaker header has a RED and Black Wire, connect the RED to the PIN ladled +5V and the black to the one labeled GRD. I still don't think it matters, but I don't have an actual PC speaker/buzzer here to look at. The piezo buzzer I have is for plugging into a solderless bread board or soldering to a circuit board. It's ambidextrous Wouldn't be the first time I got something wrong though.
The original PC speakers (real speaker not buzzer) had Red and Black wires on them too, it didn't matter which way you plugged them in though, they still worked. The colored wires were just there so people wouldn't ask which way do I plug them in. :)

Anyway, the quick way to sort it out, since its not working now, is to just reverse the plug. If it then works discussion over, I got it wrong. If it still doesn't work its either a dead buzzer, of something not right with the motherboard.