Bips is Blips without the L.
BIOS Beep Codes are what you are hearing. (BEEP)
2 Short beeps = a Ram Memory problem.
6 Short beeps = a Keyboard problem
1) Computer off, and unplugged from power.
Open the computer case, and FOLLOW Anti-Static Precautions.
Your body carries Static electricity. Static WILL fry out (Short Circuit) the delicate hardware components inside a computer.
Relieve your body of Static BEFORE reaching inside your computer.
Computer on a table, computer unplugged from power, computer case open;
TOUCH an unpainted surface, of the metal frame of the open computer case.
This action will relieve your body of Static.
IF you leave your computer in the middle of working on it, be SURE to Touch the metal frame again upon your return.
Remove all Ram Memory modules. ('Stick')
Handle the Ram Memory module by the BODY.
The Body is everywhere on the Ram Memory module, EXCEPT the gold plated contact pins on the bottom,http://en.wikipedia.org/wiki/File:Generic_DDR_Memory_%28Xytram%29.jpg
Clean the gold plated contact pins with a pencil eraser. If you are using an eraser at the end of a pencil, and not a solid eraser, refrain from letting the metal band on the pencil touch the gold plated contact pins.
Rub up, and down on each contact pin. BOTH sides. Doesn't take long. You may not see anything has been done, when finished.
The gold plated contact pins may not be bright, and shiny. That's OK. You have cleaned them, I assure you.
Doesn't take much 'corrosion' on a contact pin to make a bad contact. (Surface)
If a can of compressed air is available, use it to remove the eraser dust. If not air pressure from your mouth will be sufficient.
You can also use air to clean out the ram memory slots. Just an additional thing that helps.
Reinstall the ram memory modules. Close the computer case. Plug back into power. WAIT 1 minute, then turn the computer on.
Also try a different Keyboard. If it is a USB type, try one with a PS/2 connector,http://images.search.yahoo.com/images/view;_ylt=A2KJkK0CGWJQYW4AiT6JzbkF;_ylu=X3oDMTBlMTQ4cGxyBHNlYwNzcgRzbGsDaW1n?back=http%3A%2F%2Fimages.search.yahoo.com%2Fsearch%2Fimages%3F_adv_prop%3Dimage%26va%3Dps2%2Bconnector%26fr%3Dmoz35%26tab%3Dorganic%26ri%3D12&w=400&h=300&imgurl=forums.techguy.org%2Fattachments%2F187148d1297276771%2Fps2.jpg&rurl=http%3A%2F%2Fforums.techguy.org%2Fwindows-xp%2F979677-solved-optiplex-gx280.html&size=7.5+KB&name=Solved%3A+Optiplex+GX280-ps2.jpg&p=ps2+connector&oid=253f4bd7283ec083ce538a37ee9f6003&fr2=&fr=moz35&tt=Solved%253A%2BOptiplex%2BGX280-ps2.jpg&b=0&ni=128&no=12&ts=&tab=organic&sigr=126lumaps&sigb=138pp3ana&sigi=11ooitbdq&.crumb=ssehMErPqBD
Post back in a Comment as to the results.
(Also make sure the inside of the computer is clean)