The traces may have been broken. It's hard to tell from the picture but with as thin as they look it's a good possibility. Do you have a meter with continuity checker? The fix would be to solder a jumper wire from the solder pads to complete the trace. And is that soldered directly to the flex board?

Would a bad connection on the laser keep the disc from spinning? Or is it possible something else came lose in the process? I'm not too familiar with these. It's been years since I've been inside a Sega CD.