I have a PSC23SGR Stainless Steel Side by Side refrigerator that had a 5 yr. warrantly which just ended 5/12/11. Two previous service calls (during warranty periods) where the circuit board was replaced due to freezer temperature not holding. Now my icemaker is making ice but will not dispense through the door. The auger does not seem to be turning.

SOURCE: GE ESS25XGMC WW Side by Side

its possible that your water tank has frozen up, try turning the refrig off and leave the doors open for about 10-15 mins and try it again. if that works just reset temp controls a little lower..

SOURCE: Kenmore model 106.56702500 icemaker will not work.

You wil need to check the dual water valve at the back. However, a good place to start is by removing the fill tube from the back and make sure its not full of ice blocking the flow. At the same time have it cycling and listen for the buzz(very faint) of the water valve Call 704-932-7233 and we can ship you the part

SOURCE: GE PS123 MGNA CC Ice Auger

I just finished replacing the ice auger in my GE HSS25GFPA side-by-side and offer some suggestions/hints.
The auger (WR17X11705) was available locally (Appliance Parts Co., $28.97). This fits many other refrigerators. The replacement took a little under 2 hours. I estimate these hints may cut the time by one-half.
There are only 4 screws in the entire ice drawer assembly. It possibly was not necessary to remove the control rod. The other 3 screws hold the front cover. There are also 2 tabs holding the top of the cover.
The most difficult part of the repair was removal of the plastic assembly housing the crusher blades and the front bearing of the auger. This is held in place by only 2 large square tabs on the sides. There is enough space to get ONE side to release BUT to get both released required careful prying with thin-bladed screwdrivers (and prayer). These "tabs" don't push in, rather the drawer flexes out. Once released, the unit slides up and angles to allow removal of the auger/crusher. Re-assembly could not be easier. Stainless sheet metal screws would probably work if you do break something.
Remove the clear inside cover of the crusher assembly and the "C" clip on the threaded end of the auger shaft to separate the auger from the crusher.
And now for my PRIMARY reason for sharing my experience - the %#$@ plastic nut/bearing is a LEFT-HAND THREAD. I only realized this when trying to bend my make-shift split screwdrive back and the SOB loosened right up!
Carefully note the locations and orientations of the blades and spacers as you move them from the old to the new auger.
Good luck!

SOURCE: Kenmore Elite Trio 22.4 Cu Fridge - Flecks of "Tin Foil" in Ice

Perhaps the solution to to change out the ice maker unit

SOURCE: GE Side by Side Stainless steel Ice Maker water will not shut off

The fill valve may hae a chunk of debris such as rust in it. If you disconnect power and water, you might disassemble the valve if it's the type that was screwed together. If it's riveted, you'll have no choice but to replace. In either case, make sure you have a filter in the line so this does not happen again.