Ok, we'll work through this, it may take a few questions and answers. It may be easier than you think. How many leads does your new motor have and what colors are they?
I'm not finding a diagram for that motor. Was there one on the motor?
The old 3 connection capacitor will have to remain in place to run the compressor. Leave the compressor leads and the C lead to main power connected.
Attach the brown lead of the new motor to the new capacitor.
Attach the white lead of the new motor to the other side of new capacitor. (doesn't matter which one goes where.)
Run the black lead in and connect it to the compressor contactor where the old motor connected.
Next you need to run a jumper wire from the C terminal of the old capacitor and connect it to the white lead on the new capacitor. The other option is to connect the white lead of new motor back to the contactor where wire on C terminal comes from.
Let me know if that makes sense.