My iPhone 5 screen doesn't turn on, but the phone connects to iTunes

For a couple months, my iPhone battery has been slowly expanding from the gas inside. I should have replaced it a while ago, but I was not aware that the battery was the problem until probably too late.

So it got to the point where the screen would have white lines across it periodically and sometimes the screen would go black with the backlight still on.

Finally, a day before I was going to replace the battery, I shut down the phone and it didn't turn back on.

What is odd is that the phone worked fine until I restarted it, and now the screen doesn't work. I assumed it was because the battery had finally met its demise, so I went ahead and switched out the battery (which was severely bloated) for a fresh one.

The phone still refused to turn on, so I plugged it in and charged it for a couple hours. Still nothing. I plugged it into my PC and noticed that iTunes still recognized it as my phone. So I did a hard reset by pressing the home and sleep buttons at the same time, still nothing. I went into recovery mode, and iTunes recognized it as such, so I wiped the phone from iTunes to see if that would work.

Frustrated, I opened up the phone and disconnected the display ribbons, then plugged them back in again and closed the phone again.

Nothing seemed to work. I feel like I have tried everything in my power. Is there anything else that I can do, or is the phone doomed?

Edit: Formatting (Benjamen50)