Perhaps you've built a computer and are turning it on for the first time, or you've owned this computer for awhile. Either way, you may encounter an issue where the monitor shows a black screen and the computer is beeping. There are several causes and solutions for this problem.
Refer to your motherboard manual, since the motherboard is the beeping device. These beeps are like Morse code, and each "beep code" is explained in the manual. Common beep codes include not having a monitor or keyboard properly connected; not having a CPU fan connected, or not attaching internal power cables to the video card. This black-screen-and-beeping issue is most common with newly-assembled computers.
Check external cables to make sure they're properly connected. The most important external connections to check are the monitor's signal cable and the keyboard. If your monitor cable looks damaged or kinked, try replacing it with a spare. If your keyboard's cable looks frayed, try a spare keyboard.
Also, a PS/2 keyboard plug (round, with holes in it, about the diameter of a finger) is often color-coded purple. If you have plugged it into the green port in the back of the computer (for PS/2 mice) switch it to the other one. If there is no color coding, the proper port should have a small, embossed icon of a keyboard on the back of the computer. If it does not, refer to your motherboard manual for the correct port. If all else fails, try a spare keyboard, preferably USB (Universal Serial Bus), which can be plugged into any USB port on the back of the computer.
Check for additional motherboard power connections. Yours may require multiple cables attached from the power supply. There is the standard wide plug, which you know is connected properly because your motherboard is beeping. However, there may also be an additional, four-pin cable that connects elsewhere on the motherboard. Check the board's manual to make sure it has all the power connections it needs.
Check your internal cables. Make sure that the CPU fan is plugged into the motherboard header nearby. Without that, the CPU fan will not spin, and the motherboard may detect this lack of connection and produce a beep code. Your video card also may have one or two internal power plugs that need to be attached to the power supply's cables. These cables have unique ends on them, similar in shape to a USB plug. Refer to the case or video card documentation if need be. If those cables are not attached, your motherboard may refuse to boot the system.
Your video card may be faulty. If this is a new card, it may have arrived to you broken, in which case you will probably need to request an RMA (Return to Manufacturer Authorization) to receive a replacement. If this card was previously working for you in this system, you can contact its manufacturer yourself to receive a replacement, if the device is still under warranty.