I found someone selling a 3DS for cheap ($15), saying that the console doesn't start. Judging by the photos, the device looked really nice, with the only problem being that the digitizer was badly scratched (see main pic). Knowing that I had a fully functional (or so I thought - it has a small precision problem) lower lcd/digitizer module, that even had the red bezel (see pic #2) I decided to go for it.
I managed to fix the main problem (the device not starting) very easily - it was a matter of using a battery that still had some juice in it. I replaced the battery and the console started. However, I was unable to control it. Nothing I tried (circle pad, buttons) worked - only the digitizer was responding randomly to presses.
I replaced the broken lower module with the one that I had and everything was working fine (see pic #3) :-)
There was also a big scratch on the upper part, but that didn't affect the lcd.
When deciding what needs to be replaced, triple check if you really need to change the motherboard. I thought I needed to do so, and I remove the motherboard, only to realize that I can actually use the initial motherboard, instead of dismantling other devices.
The problem with fully removing the motherboard is that you need to uncouple the three (!) ribbons that come from the upper part of the device. The ribbons for power and cameras/speakers are easy to put back, but the one for lcd data, is very difficult. Initially I didn't connect it correctly and I realized that nothing is showing up on the upper lcd, AFTER I assembled everything.
If possible, avoid decoupling those 3 ribbons. You don't need to bother doing that, if you want to replace something from the lower part - the motherboard can be lifted, with the ribbons still connected.