iPhone 6 does not turn on; on charger - it bootloops

Hi, Im new to this board and Im not a native speaker so please be patient.

Device: iPhone 6 - 64GB

iOS: 12.4.2 (I tried to update on)

Device dropped and the screen is cracked (LCD seems to be fine).

Digitizer was not working after the drop.

Device was lying around for about two months, so the battery musst be empty.

It’s a second hand device, I’ve only got these information about the device history.

Case 1 (does not simply turn on):

1. Device is off.
2. I press the power button.
3. nothing happens.

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Case 2 (freezes after apple logo on charger):

1. Device is off.
2. I connect the device to the wall charger.
3. The display turns on immediately with the apple logo, stays for ~5 seconds
4. Display turns black again, but some backlight is definitely on
5. then no change, meanwhile there is a continues, silent zipping sound
6. I do not know if it is charging or not

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Case 3 (fast bootloop on PC connection):

1. Device is off.
2. I connect the device to my PC, with iTunes installed (USB 3.0 and 2.0)
3. The display turns immediately on with the apple logo, stays for ~1 second, My PC does not recognize any connected devices.
4. Then it turns off again, for ~5 seconds
5. Then it goes back to step 3.

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I’ve tried put it to DFU mode and restore it with iTunes, this is what happened:

1. Continues from case 3 (Step 3 to 6)
2. I press down the power and home button simultaneously , for ~ 5 seconds
3. Then I release the power button and hold the home button, for ~10 seconds
4. A “Apple mobile device” gets connected to the PC and iTunes pops up
5. Device stays black
6. iTunes says there is an iPhone 6 in recovery mode connected, offers me a recovery
7. I submit the update and recovery option.
8. iTunes unpacks the update.
9. iTunes prepares the iPhone
10. After preparation is finished the device disconnects and connects exactly two times, meanwhile iTunes says its “waiting for the device”
11. Device turns on with an apple logo, then the spinning circle appears, the loading bar appears
12. Then the device gets disconnected
13. After 1-2 seconds the device turns black
14. It does not connect anymore. iTunes waits forever..
15. And the case 3 restarts from step 3

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Can somebody make any suggestions? What should I test next?

I was thinking to order a new battery.

The Problem was really the battery.

I replaced the battery with a cheap used one. And the phone didn't turn on, it was still stuck on bootloop.

But after reflashing the os, it stared just normal.

Hope that can help somebody :)