I had a similar problem, and contacted someone who had repaired the same problem - they suggested that the LCD itself was the culprit, and, indeed, in my case, replacing the LCD was the solution. It WAS NOT the LVDS cable, though it can cause similar problems in some cases, as I understand it. Used to be the LVDS cables were hard to find (but not so bad anymore) so I was glad the LCD fixed it.
I have 8GB installed in my A1342, and it works great. Apple specs say it can accept up to 4GB, nut in real world it will run 8gb. Mine was purchased from NewEgg - this item - 1 x PNY Optima 8GB (2 x 4GB) 204-Pin DDR3 SO-DIMM DDR3 1066 (PC3 8500) Laptop Memory Model MN8192KD3-1066 - no problems at all (your mileage may vary)
NOTE CAREFULLY the position of the reed switch and its wires, so that you can replace it EXACTLY as it was removed, lest you have a series of frustrating boot/sleep problems caused by a "pinching" of the board by the top case when re-assembled. (see my comment on step 36)
BE CAREFUL that the board is replaced in the EXACT position that it was removed from. The top case has a small indentation to accommodate the small "tube" of the board. When I re-assembled my ibook I had consistent (and frustrating) boot/sleep problems, which resolved with the top case removed, re-appeared with case attached. I finally realized that this board was being "pinched" by the top case. Watch that the board sits exactly against the face edge of the optical drive, and that the wires emaerge from the SIDE rather than from the END of the board (proper alignment is illustrated well in the photos here on ifixit)
NOTE CAREFULLY the position of the reed switch and its wires, so that you can replace it EXACTLY as it was removed, lest you have a series of frustrating boot/sleep problems caused by a "pinching" of the board by the top case when re-assembled. (see my comment on step 36)
BE CAREFUL that the board is replaced in the EXACT position that it was removed from. The top case has a small indentation to accommodate the small "tube" of the board. When I re-assembled my ibook I had consistent (and frustrating) boot/sleep problems, which resolved with the top case removed, re-appeared with case attached. I finally realized that this board was being "pinched" by the top case. Watch that the board sits exactly against the face edge of the optical drive, and that the wires emaerge from the SIDE rather than from the END of the board (proper alignment is illustrated well in the photos here on ifixit)