IPad Mini stuck in recovery mode? - 1

**please actually read this before you link me to a tutorial** It's been stuck like this since last night. I've hooked it up to iTunes. I've tried restoring it from iTunes but there is an error every time. Something about the device not being ''eligible.'' I have never jailbroken it. Ive held down the home button and lock button but after that, the recovery mode screen just comes straight back on. I tried updating to the newest version of iTunes and trying it again, but this time it was even worse; the computer doesn't even register that i have a device connected now. What do i do? I want to fully restore it.
Added (1). Rex, it is stuck on the iTunes logo with the plug, not the Apple logo. I've tried turning it off countless times by doing exactly what you described, but it comes on about 15 seconds later with exactly the same screen. As i said, even if i plug it into my computer, iTunes doesn't even recognise that it's been plugged in anymore.

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