GE Bottom freezermakes little ice

Is the icemaker getting water into tray? If not>refill valve is ng
Is there ice in the tray? If so, heater element is ng and that needs replacement.

Or just get a new icemaker on the cheap at site. eBayeBay

did it sound like someone snoring in your freezer? that is your icemaker trying to eject cubes, and that noise in and of itself, is nothing to be worried about, that is normal. however, if your icemaker was failing to produce ice, when your husband removed the icemaker, was it near overflowing with ice, or did it look like it just had what would be a normal amount, i.e., the ice in the mold was little more than helfway. if it seemed like it was a normal amount of ice, then the heater on the bottom of the icemaker failed, replace the icemaker. if you had an abundance of ice in the icemaker, you may have a problem with either your water vavle solenoid not closing completely, or the icemaker motor itself is slow, causing the valve to be open too long. without checking it personally, i cant advise either way

Sounds like you need to replace the ice maker. The mold heater appears to be defective.The mold heats up prior to a ice dump. I donot believe it is worth repairing

If I understand you correctly your water line that comes through the back wall of the freezer and into the icemaker is frozen. If so you have a bad water valve. When the valve goes bad it will not seal off the water. It will seep causing a slow drip where the water comes out at you icemaker. It'd slow enough to freez causing a ice blockage. This will not allow water to come through and fill your icemaker when it calls for water.

check where the line connects at the bottom of frezzer door

change icemaker

sorry, but not unless you want to get into spending some serious time.

•  if the cubes that the icemaker makes are full size then... the water valve on the back of the machine is usually the culprit in these cases. it will not close fast enough resulting in a little overflow of water into the auger assembly every time it makes ice. it only takes a little bit of water to settle in the bottom of the pan to cause problems. 
  
• if the cubes are smaller than what you would expect then the water is leaking out right before it reaches the icemaker. either from the plastic tube behind the icemaker or the cup on the icemaker that funnels the water into the icemaker.
• it also could be the timer inside the icemaker leaving the water valve on too long.
• all these things can be tested on site. the service person must not be very well trained.

if you already checked this and think it is a different problem then let me know, i will help you figure it out. 
Mike  

are you on a well system? it could possibly be a pressure issue with the water system not dilling all the way. stuck cubes will break icemakers.