Several problems with iPhones 5S

[anon(10179112)]

Today I bought an iPhone 5s from someone who wasn't honest with me. Turns out the LCI indicators are pink, which means water damage.
She told me that the home button doens't work and that the phone shuts off at 40%.

The phone turns on and works 'perfectly' with a few flaws.

Problems:
- Home button clicks but doens't work. Touch ID works and I can get the control center to show up. I can also use the home button to get into DFU mode. Really weird..

https://www.dropbox.com/s/74ecdxdm2f7zw71/IMG_0012.JPG?dl=0
https://www.dropbox.com/s/m7qgagjkarj9y8m/IMG_0040.MOV?dl=0

- When the phone is turned off and I plug the charger in, it goes to the Connect to iTunes screen.

https://www.dropbox.com/s/y6hcmw3w5q841g5/IMG_0039.MOV?dl=0

- When phone is turned on and I plug the charger in, it will charge. But if I afterwards turn off the phone with the charger still in, the phone will turn off and go to the Connect to iTunes screen.

https://www.dropbox.com/s/5bzfj2b0m6enckq/IMG_0015.JPG?dl=0
https://www.dropbox.com/s/9tsb7drljz9ragd/IMG_0016.JPG?dl=0
https://www.dropbox.com/s/ktrxka4jbion0da/IMG_0018.MOV?dl=0

- If I restore the phone in recovery mode, it will restore it and ask me again to connect to iTunes to restore it. Sort of a loop. To stop the loop I plug the cable out once it restored. If I then turn on the phone, I get to the white 'Hello' screen and can normally install the phone.

https://www.dropbox.com/s/5864bqnc43g0xkp/IMG_0008.JPG?dl=0
https://www.dropbox.com/s/gtndi28dpgbf11z/IMG_0011.JPG?dl=0
https://www.dropbox.com/s/74ecdxdm2f7zw71/IMG_0012.JPG?dl=0
https://www.dropbox.com/s/fwifyk54lbc404k/IMG_0013.JPG?dl=0

- When I press the sleep/power button for a long time, the phone turn off, apple logo shows up, phone turns off. (don't know if this is really a problem or me being paranoid lol)

https://www.dropbox.com/s/3dt2ee3o449wito/IMG_0041.MOV?dl=0

I hope someone very experienced can help me I love all input !

 

[Just_Me_D]

I don't think you can put the device in DFU mode without the use of your home button. If you had an iPhone 7 or 7 Plus, it wouldn't be a problem since the volume up button is used in lieu of the home button.

 

[anon(10179112)]

I read something this morning about Redsn0w but I don't know if I can trust it and if it's up to date.

Link article: How to Put iPhone or iPad In DFU Mode With Broken Home Or Power Button

 

[Just_Me_D]

I don't jailbreak any of my iOS devices so I'm unaware of can be done with jail breaking tools. Hopefully, those who do will reply soon.

 

[anon(10179112)]

Turns out I was able to get it into DFU mode the normal way lol. I assumed that since the home button didn't work it wouldn't work to get the iPhone in DFU mode. Really weird that even Touch ID works and that I can get the Control Center to show up.

Anyways, I still get an error after restoring. It keeps me in a loop.

 

[anon(10179112)]

Since a DFU restore didn't fix the problem, does this mean that the problem is hardware related? Sorry if I ask a lot of questions, but I'm really eager to learn about all this.