Quick troubleshooting...
Does it even boot?
If not...it could be bad...
First, make sure power is plugged in to both computer, monitor, and power socket as well as making sure the monitor and computer are connected in a way they can exchange information
Second, make sure the mouse and keyboard work...try another just to be certain it isn't the socket.
Third, opening the computer, make sure all the RAM, cords, and cards are plugged in snuggly into their appropriate sockets...also exam RAM see if it looks damaged
And now the bad news...turn it on...listen for clicks. If no clicks...you might be in luck, if you hear one, even slight...it means your hard drive died. That happened to me once...stunk to high heaven, I think that one had 3 beeps as well.
Even worse, if it doesn't even boot period, it could be a motherboard problem...to see if that is what is occurring, try to get to Bios.
The best way to get to Bios is to do it as the computer starts up...if you can't get to Bios, that's usually a really bad indication of either your powerbox is dead, your power supply is somehow cut off, OR, your motherboard died.
Before thinking it is definately your motherboard, MAKE ABSOLUTELY CERTAIN your computer monitor is hooked up to your computer. If your computer has lights on...but nothing on the monitor, your computer might be fine, your monitor might not be.
However, determining whether it is your power or the motherboard without actually being there is rather tough to do.
Also, reverify that your keyboard actually works. It's rather hard to press alt f8 or whichever way you are accessing bios if your keyboard isn't working.
Now if you can get to Bios, you are scotchfree. In Bios, you can see what the computer sees, and what your computer says is dead. If it can't see your RAM, it's a good indication that's what died, or if your hard drive doesn't register (like what happened to me once) that's also a good sign.
However, before panic, remember, check to make sure it's not something simple like keyboard, mouse, or power problems. Be a shame to replace a motherboard or harddrive when one only had to plug in the keyboard. Most likely it's going to be a keyboard or mouse problem...especially if it gets past the opening screen, but then has a little not about not seeing it, and several beeps.
According to the list Javora posted, it's going to be either a keyboard or Video problem. So check to make sure your card is working (should default to generic drivers I'd imagine if you have a backup card or anything and enable it I'd imagine). Key thing is to see if the light on your computer is lit and then use the beep code.