iPad Not Working; Battery Causing Restart after Screen Replacement

Good Afternoon

I own a 3rd generation iPad Wi-Fi model with 16GB onboard storage. Originally, it belonged to my sister, and the digitizer became cracked after the device fell to the floor, and my brother-in-law successfully replaced it. However, a short time after he had replaced it, the new digitizer also cracked. Not wishing to spend more money on an aging device, they opted to buy a new one, and offered me the cracked one, if I wanted to fix the digitizer again.

So, I bought another new digitizer, and went through the motions of repairing the device again. Since the digitizer had already been replaced, removing the front was not particularly challenging, however, the wi-fi antenna ended up sticking to the digitizer and the foam underneath was torn. I fear the antenna might be damaged, but I cannot tell, since after I installed the new digitizer and replaced the screen, the device did not appear to be turning on, and it was not even making noise.

To see if the device was even powering on, I connected to my Mac via USB and found that something peculiar was happening; the device appeared to be rapidly turning on and off in a pulse-like pattern. I have Dropbox installed, and it pops up every time a USB device is connected, however, when I connected the iPad, this popup kept appearing and disappearing as if I was plugging in and unplugging the iPad constantly.

I decided to dig deeper, and removed the logic board, to inspect if there was any damage to it that I may have inadvertently caused. I could not see any (though my expertise is more in software than hardware), and began to secure it back to the frame. As I was doing so, I had left the device connected to the computer, and found that it was no longer powering on and off rapidly, and was staying connected, but as I screwed in the battery connector, it began power-cycling again.

As such, I pulled the logic board away from the battery connector, but left the 30-pin port, speaker, and home button connected, and found it was staying on. In spite of this, I tried connecting the lock button and screen. When both were connected, I clicked the lock button, but the screen would not illuminate (or even turn on for that matter). I can verify that the lock button is working, as I have made several attempts to restore the device via the lock+home button combination, but the restoration has failed because of the power-cycling, and the device is locked behind a passcode.

If anyone has any suggestions as to how I might be able to resolve this and get the iPad working again, it would be greatly appreciated. If it is completely fried, it's not a huge deal, since the device is already 5 years old, and doesn't owe me anything, but I would like to get it going if I can.

Thank you in advance.