2003 Toyota Corolla Car Won't Start (No Sound At All)

Here's the deal. My car wouldn't start. There was no sound at all. I tried jumping the battery, that didn't work. The battery seemed fine. The lights, wipers, and radio all came on just fine. I got AAA out to look at it. The guy took a long metal rod and started banging somewhere below. Sure enough the car started. I asked him what he was banging on and he told me the starter. He said, "The starter is worn. You're gonna need a new starter". I asked him again EXACTLY what he was banging on and made sure I saw the exact location he was banging, which was at the BOTTOM, BACK of the engine. He said, "I'm banging on the motor". So, I went to Autozone and bought a new starter. I took out my Haynes manual to attempt to replace it and low and behold it says that the starter is on the bottom, FRONT of the engine (by the radiator)...not the back part where he was banging. I got underneath the hood myself and looked and sure enough the starter is in the bottom, front by the radiator. This is not where the guy was banging. He was banging on the bottom, BACK, yet he told me he was banging right on the starter motor. So, my question is, do you think the problem with my car not starting is still my starter? Or, could it be something else? Could him not banging on the starter itself and instead banging in the back of the engine still mean the starter is what is bad or could it be anything else? I want to make sure I replace the right part. Thanks!!