Phone seems dead, possible way to recover data?

Hello everyone.

I have an iPhone 5s, about 22 months old, which seems to have suddenly given up on life. I don't necessarily want to fix the phone, I only want a temporary fix to have it running maybe an hour to recover a phone number and a few photos. I used to backup to my computer almost daily but the phone died before I could get it out of the phone. I was already thinking of switching to a newer phone, and it's already dead so I'm not worried about putting the last nail in its coffin.

What happened:

I was driving, phone plugged in a 12v car charger, playing music. The battery was reported to be at roughly 50% when the phone suddenly died, not the way it usually shuts down when the battery is too low... More like yanking off the power cord of your TV. A few days before, I've had issues where I had to plug/unplug the cord to get it to charge. The phone NEVER suffered water damage, but was dropped 2-3 times, but not recently.

What it does:

Nothing, litteraly nothing. Will not charge, power on, show the low battery icon, plug in to iTunes logo... Expensive paperweight at the moment. Will not show up on the computer.

What I've tried:

Using different chargers, official and not, charging using computer.

Using different cables (all official Apple cables)

All combinations of reset/hard reset.

Recovery mode

DFU mode

iTunes recovery (will not be seen by the computer at all)

Tried to charge it for 48 hrs straight.

Talk to Apple support.

Nothing from the above worked.

What my research has led me to:

Battery could have crapped out completely.

U2 ic faulty

The world hates me.

Any suggestion on what I could do, DIY style. I do not want to spend 100+ on repair when I could get another working phone for that price. As stated before, I only wish to bring back to life for one last time.

I have read about removing the battery and charging it directly with 4.something volts.

Any ideas, previous experience from all of you people?

Thanks in advance for your help.

P.S. English is not my native language, I hope it is clearly written though.