In simple terms, you have a hardware failure, probably in your motherboard, hard drive or memory.
The beeps your hearing, are there for a reason. The way it works, is, when you first turn a computer on, it goes through a "Power-on, self test", (know as a POST).
During this period, the BIOS queries the system hardware, such as the hard drive controller, the i/o ports, the memory, etc. and expects to receive back a specific return code which indicates that the specific hardware is running properly.
If it finds a failure in some element of the hardware, it will issue a specific pattern of beeps to tell you which part of the system is failing. (It does this because the system may be unable to display the error on the screen).
Each of the different BIOS manufacturers (BIOS is an acronym for "basic input output system, the hardwired code that talks to the actual hardware), have their own series of short and long beeps, for the different type of failures. So to know where the failure is, you must first know what BIOS manufacture you have in your computer.
Some of the more popular manufacturers are: AMI, Award, IBM, Phoenix, Macintosh, etc.
When you first turn on our computer, the display will report which brand of BIOS you have, and its version.
Once you determine the brand, you can go to any number of web pages that have a cross-reference for the beeps for each brand on BIOS.
I think most adhere to the old IBM PC beep codes as follows:
No beeps: no power, bad CPU,
1 beep: normal
2 beeps: POST/CMOS error
1 long beep, 1-short beep: motherboard problem
1 long beep, 2-short beeps: video problem
1 long beep, 3-short beeps: video problem
3 long beeps: keyboard error
Several long beeps: memory failure (most common fault)
Continuous hi-lo beeps: CPU overheating
You can check with the following websites to get an idea of what's going wrong.
Computer POST and beep codes
How to Diagnose Computer Beeps eHow
Often times a SIMM has come loose in its slot (or corrosion on the connector tabs). If your getting a memory error, you can try opening the box and try re-seating each of the memory Simms to see it that might be the problem. (When you have them out, look at the row of pins along the bottom and see if any look corroded.)