I'm a Dell accredited and Microsoft certified engineer. Not just to show off or chat you up - cause I know girls love geeks - but so you know that I know what I'm talking about.
The beep you are hearing is an error code from your motherboard. Basically it's not getting past the P.O.S.T. or power on self test. The reason the beeps still sound without your speakers plugged in is that there is a small system speaker build inside you case to do just this.
Without the make and model of the motherboard I can't tell you what that specific code means because they vary. The model you found was from your power supply which is where the power goes into the PC.
You can find the make and model of your motherboard by inspecting the main board which everything connects into. It'll likely have a name like gigabyte, Asus, pc Chips, Foxcon etc on it and then on one of the edges some alpha numeric model number.
Once you have your make and model number of your board you'll need to find out what kind of Bios it has from the manufacturers website. Finally you'll need to decode the audio error code with this;
http://www.pchell.com/hardware/beepcodes.shtml
it's by no means complete but it's got the usual suspects on it.
The other method would be to try and take your computer down to the most basic setup and see if it boots up. In other words, single stick of memory, motherboard, power supply, cpu and cooler. If you don't have on board gfx the card then disconnect you gfx card too cause you don't need to see the visuals to see if it'll boot beyond the usual beeping.
If that doesn't work it'll be one of the main components. Memory can be got fairly cheap as can a processor if you get them on ebay but motherboards are sometimes more tricky to get to match up with all your other components.
Let me know how you get on and if you have any other questions. Or if you live anywhere near Inverness in the Highlands of Scotland I could arrange to come by and check it out.... I've a feeling you're not near though.
Good luck,
R