Car Won't Start with a Jump. Battery,starter, or Alternator?

2004 Cadillac CTS Car won't start. Turn the key and no click. Had friend jump with cables. Gave the car lights but won't click over. Makes a click and then a small winding noise.

Suggestion:

it,s not the alternator so it has to be either the battery not taking the charge or the starter is stuck. did you clean and tighten the battery terminals?

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