Ipad stuck in a boot loop

A couple days ago, my IPad restarted itself. This happened everyday after that. Today I tried to factory reset it but it got stuck on this screen:

So what I did was go to the website and followed the instructions. I Pressed and quickly released the Volume Up button. I Press and quickly released the Volume Down button. I Pressed and held the Top button until the device restarts. The first time it didn't work. The second time it didn't work. I've tried it many times so far but it doesn't work. So next I tried the ITunes method. First I tried to update it, but then this message popped up:

Then I tried to restore it. then this message popped up:

The message popped up but it still extracted the software. It did put in new software but then after that process was done, this message popped up:

I've done those steps about a 100 times now but still my IPad does not want to work. I can turn it off with the power button and the volume button, but it doesn't get factory reset. I have no idea what to do now. I even took it to an apple store, but they just gave me a dumb offer about how if we trade this one in we can get another one. But I wasn't about to spend $400 more on a $400 iPad. This IPad has been lying and gathering dust for a long time. Any solutions?