I have a lg frige model #lrbn20512ww. it quit cooling both upper and lower yesterday. are there any known problem with the compressor or could it be somthing else. the compresor runs for about min the shuts off.

check capacitor to compressor if ok possible bad compressor if no voltage to compressor bad board

What is the model number?

IS the compressor running and is it hot?

Small refrigeration units like this one like to fail to cool by developing a small leak and slowly
leaking refrigerant.
THERMOSTAT FAILURE CHECK:
A technician will check the thermostat using using a DMM (digital multimeter). But you can suspect the thermostat if you set the thermostat high and the compressor motor does not run,
then set thermostat low, and the compressor motor also doesn't run - in other words, the thermostat is failing to start the refrigerator's refrigeration system no matter what its setting - an obvious failure of the thermostat.
COMPRESSOR FAILURE CHECK:
If the compressor is dying, you would hear the compressor running almost constantly, but not
sounding quite right (uneven noise, clunking, tapping).
REFRIGERANT LEAK CHECK:
If you unit is low on refrigerant (due to a leak), the compressor motor will be running
almost constantly, but it will sound Ok.

you need to have the defrost element (s) replaced

your rtc overload on the compressor is getting weak and drops out and this shuts power off to unit and you need to replace it,its plugged into the side of the compressor located in the lower rear of the unit,simply unplug frige,access the compressor,remove retainer spring,unplug rtc overload and replace it

May be the glass heater for defrost not function cause by thermal fuse broken, or may be the defrost timer damage. The timer location usually at the back of reff on the bottom side, over or near the compressor unit.

compressor shuts down air is cool but unit does not stay long enough to cool lower the thermostat down little lower if the compressor starts up then bad thermostat

U need a new wr51x10101 heater harness 35.50 $ there is an ice build up on your coil defrost coils replace the heater harness U should B good to go

I need to make sure that your refrigerator model and make numbers are listed correctly. Im having trouble with the information listed above your comments. I have GE data base and want you to look at the hyper link listed below.  and let me know if this or I can help lead you in the correct direction, Thanks, Sea Breeze
http://www.appliance-parts-warehouse.com/general-electric-parts/General-Electric-Refrigerator-Parts-Page-6901.cfm