iPad only shows restore screen, only when on AC

About 3 weeks ago, I was given an iPad 7th gen that had been dropped, repaired, dropped again, and for whatever reason, the repair shop wouldn’t touch it any more. When I obtained it, it showed the following problems:

1. Digitizer cracked to all !&&*.
2. An odd-looking, out of place cable was visible between the digitizer and the LCD screen at the bottom of the unit, near the home button.
3. iPad only boots to the “trouble” screen (showing https://support.apple.com/ipad/restore), but would only boot when connected to A/C power. It had been sitting dormant for a while so I figured the batteries have completely discharged.
4. Completely unresponsive, won’t boot at all, including to trouble screen, when on battery or connected to a PC or Mac. I tried with two different PCs and two different Macs.

I (foolishly) sent it to Apple for repair, who sent it right back, rejecting the repair due to the 3rd-party repair, which, at the time, I was unaware of.

When I got it back, I decided I’d try to fix it myself. I opened it up, and noticed the following:

1. The cables from the digitizer to the logic board had been severed, most likely during one of the previous repair attempts, and the connectors on the logic board were missing.
2. The cable from the home button to the logic board was been removed, which I wasn’t able to identify from before when I saw it sitting between the digitizer and the LCD. The cable and the home button appear to be in good shape.

I replaced the digitizer, reseated the home button cable, but it still had the same symptoms as above — only booting to the trouble screen, only when connected to A/C.

I attempted to do a DFU restore, which it appeared to partially accept, but the DFU restore ultimately failed with 4005 error. Here’s the entries from the log:

[14:37:08.2144] <DFU Device 0x600002d54460>: operation 2 progress 99

[14:37:08.2145] Issuing DNLOAD request

[14:37:08.2161] Issued GETSTATUS request: state = 5 status = 0

[14:37:08.2162] Issuing DNLOAD request

[14:37:08.2167] Issued GETSTATUS request: state = 6 status = 0

[14:37:08.2679] Issued GETSTATUS request: state = 7 status = 0

[14:37:08.3259] <DFU Device 0x600002d54460>: DFU succeeded

[14:37:08.3263] Finished DFU Restore Phase: Successful

[14:37:08.4277] DFU mode device disconnected

[14:37:08.4277] Device removed when in state Restoring, moving device to transition state

[14:37:08.4277] Changing state from 'Restoring' to 'Transitioning'

[14:37:08.4277] Creating timer to monitor transition

[14:37:08.4277] Creating a timer for 10 minutes

[14:47:08.4494] Timer fired to timeout transitioning device

[14:47:08.4494] Changing state from 'Transitioning' to 'Disappeared'

[14:47:08.4495] Device disappeared during transition

[14:47:08.4495] Device isn't booted but USB is up.

[14:47:08.4512] Restore completed, status:4005

[14:47:08.4512] Failure Description:

[14:47:08.4512] Depth:0 Code:4005 Error:Gave up waiting for device to transition from DFU state to DFU state.

Finally, I let it sit on AC power overnight hoping that would be sufficient to charge the batteries enough so that I’d be able to complete a DFU restore. However, even after the overnight charge, the moment I remove it from AC power, the LCD shuts off, and the unit is completely unresponsive.

My best guess, at this point, is that the either the battery is defective, or that the battery is completely discharged, and a hardware fault is preventing it from taking a charge. Hence the DFU restore failing because the iPad never wakes back up after DFU. I checked the screw holding the logic board to the battery, and there appears to be a solid connection.

If it’s something as (relatively) simple as replacing the battery, I’d like to attempt that repair myself. If there’s a hardware short on the logic board which is preventing the battery from taking a charge, that’s something above my skill level and I’d want to take it to a shop to repair.

Short of proactively replacing the battery myself, is there any way I’d be able to diagnose which issue it is? Am I missing something in my diagnosis, and it could be some other, unrelated problem?