Half of the screen doesn't work!

The first thing you would try would be to check if the cables are correctly in place. Open up your phone, disconnect the battery, then unplug the screen cables and reconnect them again. The next thing you would try would be a new screen. Try replacing your screen with this guide iPhone 6 LCD 및 디지타이저 교체

Then, if that doesn’t work, then if would be a problem with the touch IC. You mentioned that your phone was bent. Can you see any weird grey bars on the top of the screen? That is often a symptom. Having a bent phone can damage the touch IC and display ICs, which stops the touch screen from working. If a new screen doesn’t fix it, I would suspect it is a problem with these ICs. It is a common issue in the iPhone 6, Bring it to a micro-soldering repair shop, and they should be able to fix this.