2001 accelerator quits working

My brother has a 01' cavalier that has been giving him trouble, hope someone on here can help me out. It all began when it wouldn't start, but could be boosted. He had the battery and the alternator checked out and was told they were fine, but on his way home from college for spring break he said it quit on him 3 times. After setting on the side of the road for a few minutes he said it would start just fine. He said one time he was using his cruise control when it seemed to turn itself off and the car began to decelerate. According to him the engine did not shut off, but he said when he tried to accelerate it was unresponsive and continued to decelerate. It's sure got me puzzled. Any and all help is appreciated.

loose ground wire. clean connections on battery and trace the ground wire and clean the surface it connects to. if it has no consistency, then check that.

also all of the main grounds at the starter mounting bolts