Car wont start put a jumper box on it?

Here are a couple of videos I hope this helps.

I just bought the new battery from Walmart, it sounds like it's getting power to it okay. And like I said when I first went to get it the guy put the jumper box on it and it started right away, sounded excellent. But I couldn't drive it cause the control arm was jacked up.

So I had to have a transport guy pick it up and he said that he tried to start it but couldn't ever get it started. Not sure what happened from after I started it until it got delivered but something has happened. So the control arm is now fixed, bought a brand new battery, and now it just clicks really fast when I try to start it. I had someone look at the starter, but he isn't a mechanic so I don't know if he really knew what he was doing or not. And yes I did clean the very little bit of corrosion that was on one of the cables. This just really sucks. I am trying to get moved and can't until this car gets fixed.

Do you really think it's the battery?

So I had that battery checked and you're right it was a bad battery. But now it's a new one and it's still doing the same thing. Gosh this so frustrating.

And yes I lose electrical power, I can't tell really where the clicking noise is coming from but it sounds like it's coming from the area in the video I just uploaded. It does have a good battery, and it's got a good connection. Everything is clean as far as the connectors. It just makes no sense cause when I bought it, I myself heard the car run after that guy jumped it with his jumper box and it ran perfectly fine. The motor sounded brand new. And I get it home and now this?

One other thing that is important to note, when I try to start it, the only time that the air, radio, and all the lights really come on, well that's not happening now. Maybe 2 times has everything actually ever came on, like the whole dash, otherwise it's not all coming on.

Now also, so this car has a push start button, but it doesn't look like it came from the factory, but on the key fob it's like a regular key fob, yes it has a key in the fob but that only goes to the doors. I'm wondering if this push start button is working right? It just doesn't look like something a factory would put in it.