Likely you have a high resistance point between the battery and the turning of the starter. You can use your jumpers to jump from the battery directly to the starter positive, and a good negative, and if that works you have eliminated the starter as the problem and so it's in between.
Totally check the negative and positive connection to the starter. That is your most likely point of failure if the starter proves to be good with jumper cables.
If it doesn't, likely starter brushes have worn down and need replacing. The springs can't provide enough pressure when the brushes get short, and the starter just burns instead of turns.