Beeping is normally an indication that something needs your attention, but - as you've seen - determining what that something is can be a whole other world. You need the make and model of the server first and foremost, as the beep codes could be different depending on these factors.
Now looking at the logic of it, the server is still running, so whatever it is that needs your attention is something that the server can remaining operating despite a failure or imminent failure of. This indicates something that there is more than one of, commonly either a hard disk, a CPU (if more than one), a memory bank or a PSU.
If it's a HD, and again depending on the make and model, there may be lights on the front panel to indicate this, and which HD it is. You'll be looking at a front-mounted drive caddy, with each HD in it's own slot, and each with at least one light, which may be green, orange or red.
If it's a PSU these will slot into the back, and should again have lights. You can recognise these cos the power leads are going into them. ;)
If it's one of the others, there may or may not be a front status panel giving more info, or even just an error code (e.g. something like e1211 if it's a Dell). This may also have either a green, orange or red light or be backlit in one of these colours.
There may also be a diagnostics program installed on the server which could pull out the info, but to run that you'll probably need Administrator access which I'd guess you don't have.
So based on this you can do a certain amount of fault diagnosis, at least to the extent of determining what it's not. After that - STEP AWAY FROM THE SERVER. Kudos to you for trying to be helpful, but if you try to do any more work here you'll be a person who is not authorised to do this work who is taking on responsibility for something that ain't your area of expertise, so you need to hunt down your sysadmin and explain why he owes you a beer. :)