Crashed my Mini 2 a while back, and I don't have the DJI Care warranty. Besides snapping the propellers, there wasn't any significant visible damage to the arm or motor. When I tried to take off again, all the motors spin fine except the left front. And the LF motor is actually spinning itself, and when I try to take off from my hand, while holding the drone so it can't take off, the motor would spin perfectly fine and look like it was functioning just like the other 3. But the LF motor is doing something wonky, the dorne will not take off. It kind of flips over, as the other 3 props produce lift and this one does not. Strange because it looks like it's spinning fine.

So, I replaced the motor, and I'm having the exact same issue. The way the new motor sits on the old arm indicates that there may be something out of whack with the arm. What I mean is, there's a very tiny (like .5mm maybe) difference in the gap between the motor and the arm is sits on, so it would not be perfectly level. My next move is to replace the arm.

My question is, should I be looking at anything else that could be broken here? A ribbon cable inside, or something? I hope this arm solves the issue, but I'm not counting on it. I'd like to hear from those of you that have more experience repairing these drones and get your opinion.  

Best bet is that you have the wrong propeller blades on the motor OR you wired the connection the wrong way around.
I believe that these motors are essentially 3 phase motor and that reversing any two connections will reverse the motor. However assuming you replace the motor and wiring I would have a look at a couple of teardown videos on you tube and look and see if you can see the correct order in which to solder the wires to the board to solder.

I think you will find the attached shows the correct rotations and I think it is important for yaw control that the motor do rotate in these directions.
If you do have a motor turning in the wrong direction, let's say its turning clockwise, then clockwise prop would cause that motor to generate lift but I think it would screw up yaw control.

Hi, asuer888. Sorry about what happened to your drone. DJI consumer drones have 1-year warranty. If you want to send the drone to the DJI repair center, you can use this link:https://repair.dji.com/us/repair/index. The warranty can be applied depending on the assessment's outcome, including your unit's warranty period. We appreciate your great support.