Hyundai Repair: 2004 Santa Fe Starting issue, cylinoid, battery cables

Question
I have a 2004 Santa Fe 2.4 liter 4 cylinder. Yesterday, I went to start it and it wouldn't turn over. Every time I tried to it just made a clicking noise. Checking the battery, it said that it was low, so I charged it. The battery is now full, but the car still won't turn over and is still making that ticking noise.

I'm worried that it's the starter or the cylinoid that is the the issue. My local auto parts store said that if I can take off the starter and bring it in that they will do a check on it to see if that's the issue. The problem is, I'm unsure where the starter is. Can you please advice me to where I can find it.

Also, do you have any other suggestions on what else this problem might be if it isn't the starter or the cylinoid?

Thank you!

Answer
The starter is located under the exhaust manifold and is bolted to the transmission.

My primary suspicion is that the problem is with the battery-- i.e. that it won't properly charge.  Unloaded battery voltage isn't particularly relevent, but if you have a voltmeter, there's a simple test you can do.  Read the battery voltage when attempting to start the engine.  If it falls below 10V, you likely need a new battery.  I suspect this even more if the original battery is still in the vehicle.

Other potential causes would be defective positive or negative battery cables, poor connections at either cable end, defective transmission range switch, or poor contact or excessive resistance anywhere in the solenoid circuit.