1987 Jeep Cherokee Jeep want Start

I HAVE A 1987 JEEP CHEROKEE I HAVEING A PROBLEM GETTING IT STARTED IT WAS ACTING LIKE THE BATTERY WAS DEAD IT WOULD START UP BUT IT ACTED LIKE IT WAS NOT GETTING ENOUGH POWER TO TURN THE MOTOR OVER BUT IT WOULD START. BUT ONCE IT TURNED OVER AND STARTED RUNNING IF YOU KILLED IT I WOULD START BACK UP WITH OUT ANY PROBLEMS. IT ONLY ACTS LIKE IT DONT WANT TO CRANK IF IT SETS FOR A COUPLE HOURS NOW IT WANT START AT ALL.THE BATTERY TESTED GOOD ON THE JEEP SO I TOOK THE STARTER OUT AND THEY TESTED IT AT THE PART STORE AND THE SAID IT WORKED. I HOOKED IT BACK UP TO MY JEEP AND TESTED IT WITHOUT BEING INSTALLED IN THE CRANK CASE THE STATER WOULD ENGAGE BUT THE MOTOR WOULD TO TURN ON THE STARTER. SO SHOULD I STILL REPLACE THE STARTER? IF NOT WERE DO GO NEXT TO LOOK FOR THE PROBLEM OR WHAT SHOULD I TRY REPLACEING?