Error 4005 when restoring iPad 4 in DFU mode
So my aunt got a new iPad Mini 4 to replace her old iPad 4th gen. She told me if I could fix her old iPad she'd think about handing it down to me (glad iOS 10 will support it haha). She took it to the Apple Store and they said it would be a $300 fix due to a hardware issue. But I am certain that it's a software problem. The screen lights up but no further progress is made. So, I put it in DFU mode and tried to restore it. But I got error 4005. I'm so frustrated right now. I really want to fix it because of her promise to consider handing it down to me. Any help is appreciated.
UPDATE: Battery was dead - that was cause for error, I think. Now I have it plugged into wall outlet, and as of 7:41 ET it has the black screen with battery icon (4 horizontal red bars in the icon) and has been this way for half an hour. How long will I have to wait for it to charge enough to power on? The 4005 is currently not a problem and I don't think it will be in the future.
UPDATE 2: It powered up, now wants me to "Connect to iTunes" (the screen with the iTunes logo and Lightning cable illustration). So I will - it's probably to restore it.
UPDATE 3: It is now charged enough to boot but it displayed the connect to iTunes screen. I have connected it to iTunes and am performing a restore with an IPSW file for iOS 9.3.2. The extraction worked, now the iPad is showing a progress bar under the Apple logo. Progress bar currently empty. Will update. EDIT: screen went black, stuck at Waiting for iPad, so I quit iTunes (I'm on a Mac) and plugged the iPad back into the wall outlet - I think it ran out of battery again because I didn't let it charge long enough.