Starter won't run on '02 Hyundai XG350

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Occasionally(but inconvientally)the starter won't turn over; albeit the battery is new (3 months), connections are tight, lights and alarm bell operates. You turn the key and all you get is silence...no cranking! Whats the appendage on the positive terminal that connects to the battery. At this location, the wiring splits in two paths; I suspect one path to the lights, radio etc. and the other to the starter solenoid/starter, but I have no schematic. I need to know what components are in the starter circuit to troubleshoot this. Has anyone also experienced this?