Beeping while door is closed

It looked like your model does NOT have an external ice/water control panel which has caused beeping problems on some models.
For your model I would try the following....
Door Alarm
The main cause of a beeping GE unit is an open refrigerator door. Some models are equipped with an internal door alarm, which trips when the door remains open for 3 minutes or longer.
One way to check this .... put your smartphone in the refrigerator on video mode and close the door. The light should go off with the door shut. If the video shows that the light stayed on when the door was closed ... then it reinforces that something is wrong with the switch/alarm. Repeat video for the freezer.
Door Seal
If beeping persists after the freezer or refrigerator door is closed, the door seals may be blocked or so dirty that the internal door alarm is tripped. The seals can be cleaned with a soft cloth and warm, soapy water. Also, an item inside the refrigerator may be preventing the door from fully closing.
Cooling System
Reactivating the refrigerator's cooling system includes a beeping noise. When the refrigerator is off, the "Off/Off" light appears on the door display. When the "Adjust Freezer" and "Energy Saver" buttons are held down for approximately 3 seconds at the same time the beep sounds and the "Off/Off" indicator disappears. Hold the "Ice Off" and "Freezer" buttons to activate the cooling system inside of the fresh food compartment. A beep signals the system is activated. The beeping should stop after the cooling system turns on. If it fails to stop, try unplugging the power cord to reset the connection.
Power
The GE's internal door alarm can get stuck. Try unplugging the refrigerator for about 10 seconds and then plug it back in. If the beeping continues, the internal door alarm might be broken or defective. Contact the manufacturer or a technician for further assistance. One way to check this .... put your smartphone in the refrigerator on video and close the door. The light should go off with the door shut. If the video shows that the light stayed on when the door was closed ... then it reinforces that something is wrong with the switch/alarm.

Good luck on your troubleshooting!

What is the exact model number? This may be an issue with the cables that connect the door to the power supply.

Fridge keeps beeping or buzzing: The following is for Frigidaire models but others can be addressed similarly.

Several Frigidaire refrigerator models have an electronic control panel on the freezer door the owner can use to adjust the internal temperature, dispense ice and water and receive notification about issues such as the need to replace a water filter. The refrigerators also emit a beep for various actions and as an occasional alarm. Determining what causes the beeps necessitates some troubleshooting.
Temperature Controls ·A Frigidaire refrigerator's display panel blinks when the control panel is touched to set temperature controls. After pressing "Freezer Temp" or "Refrigerator Temp" on the keypad, press the arrow buttons within five seconds to increase or decrease the desired temperature. If you do not press the arrow buttons within five seconds after pressing "Freezer Temp" or "Refrigerator Temp" on the keypad, the refrigerator beeps to indicate the current setting will stay in place.

Door Open ·When you leave the refrigerator or freezer door open, the refrigerator beeps. Also, the "Door Ajar" indicator illuminates on the appliance's display panel. Shutting the door and pressing "Alarm Reset" stops the beeping and turns off the "Door Ajar" indicator light.
·The Frigidaire refrigerator has a control lock feature that prevents use of its control panel or dispensers when the unit is locked. When the control lock is active, a beep sounds when a keypad or dispenser is pressed. Release the control lock by pressing the "Control Lock" icon for three seconds. A beep will sound, and the icon's light will go out.
Power Reset ·A power reset is occasionally necessary if the Frigidaire refrigerator's control panel does not work normally or a reset function on the keypad does not work. A power reset involves disconnecting power to the refrigerator by unplugging its power cord from the electrical outlet, waiting 30 seconds and plugging the power cord back into the electrical outlet. When the control panel resets, a beep sounds. If the refrigerator beeps even after a power reset and the beeps' source is not known, contact Frigidaire.


Read more :http://www.ehow.com/info_12148688_cause-beeping-noise-frigidaire-refrigerator.
Cause of Beeping Noise in Frigidaire Refrigerator eHow

Here is a good link on this subject:
Cause of Beeping Noise in Frigidaire Refrigerator eHow

If it is cooling OK, try unplugging and leave it for 5 minutes but if the beeping returns and everything is normal, it could be a problem with the control board...


similar issue no freezer:

Hi Hope, usually when the door(s) have been opened for longer than 10 minutes, an audio alarm sounds and the interior lights shut OFF. This protects the liner from melting due to the heat produced by the light bulbs. The alarm will sound every two minutes until the doors are closed. Once the doors are closed, the alarm is reset.

The refrigerator will also beep on some models to inform the user that the door has been left open and the cool air is escaping.

If the alarm keeps on going off after the doors have been closed and unit has been reset, I recommend contacting a professional technician so they can diagnose and repair your refrigerator.

Is this a door alarm? ARe you sure the temperatures are good? or are they sort of ok, indicating it is getting warmer. the filter is only for the ice maker and the water dispenser.

could be just vacuum caused by temp diference if you shut hear noise then try to open quickly but is stuck shut try pushing seal so it breaks from surface. if door opens easy then this is normal on some makes. also be aware if frot free when you close door fan comes on. May be getting noisy bearings.

If this is listed under the right model, then the only thing it could be is some models have a
door alarm,that will beep if the door is not closed. You could check and clean the gasket.
Or it the switch that tells the fridg that the door is closed. Check if there is a top door adjustment to bring the door closer to the fridge where the door hinge is. This might apply or push on the switch more.

Open door and turn power off then on twice. Then press the Overtemp reset.

Unplug your refrigerator from the ac outlet, and 0open theref door for approx. 5 minutes. Then plug it again, after you hear the beeping close the door. wallah it's fixed.