The beeps you hear are BIOS Beep Codes. The computer's way of telling you something is wrong, and the area to look into for it.
For one example: One long beep, followed by two short beeps. Then a small period of silence, and the beep code starts over.
Without knowing the beep code you hear, it's like shooting in the dark when giving a diagnosis.
Also wish I had the Model Number of your Gateway desktop computer to help you further.
This is up on the side of the computer tower, or on the back.
Model: Gateway 7200X.
S/N = Serial Number. DO NOT give this out in a public forum. Only to a Gateway representative, or Gateway Support online ]
If I were to take an educated guess, it would be a problem with your graphics, or Ram Memory.
I would suggest opening the computer case, and removing all Ram Memory modules, then cleaning the gold plated contact pins on the bottom.
Clean the contacts with a pencil eraser.
Power unplugged to the computer. Work on a table. Unplug all cables to the computer. Open the computer case, follow Anti-Static Precautions.
(If you are not perfectly sure where the cables go, I advise making notes, and a drawing of where they go before you unplug them)
Your body carries Static electricity.
Static WILL fry out (Short Circuit) the hardware components inside a computer.
[ Some hardware components examples are; Processor, Ram Memory, Harddrive, Graphics Card, and Motherboard's chipsets ]
TOUCH the metal frame of the open computer case.
This action will relieve your body of Static.
Computer unplugged from power, you are safe.
Touch the metal frame, your computer is safe.
Should you leave your computer in the middle of working on it, upon your return be SURE to Touch the metal frame again.
This is a basic example of a Ram Memory module, ('Stick'),http://en.wikipedia.org/wiki/File:Generic_DDR_Memory_%28Xytram%29.jpg
(You can left-click on the photo to enlarge. You can enlarge twice)
Note the gold plated contact pins on the bottom, of the Ram Memory module.
These are the contact pins you clean with a pencil eraser.
You don't have to rub the eraser on the contact pins very hard.
Just go over the contact pins with the eraser.
If you are using an eraser on the end of a pencil, refrain from letting the metal band, contact the gold plated contact pins on the Ram Memory module.
After you clean each contact pin it may not look like you have done anything. You have.
Corrosion builds up on the contact pins after time. It takes very little corrosion to make a bad contact on those contact pins.
Use air to remove the eraser dust.
If you have a can of compressed air for computers available, this will work.
If not air pressure from your mouth will be sufficient.
Reinstall the Ram Memory module/s.
Reinstall the computer cover.
Plug the computer back into power.
WAIT 1 minute, turn the computer on.
Gateway Support > All desktop models,http://support.gateway.com/support/supinfo/index.asp?pg=2&file=dt.html
Video of how to remove, and reinstall Ram Memory,http://www.videojug.com/film/how-to-install-more-memory-in-my-computer
[ You won't need an ESD wrist strap following my Anti-Static Precautions above ]