If you saw smoke, there are probably multiple issues. Smoke usually comes from the battery, which is why you are having a power issue. The smoke could have damaged the screen as well as caused the backlight issues. I would examine the motherboard for any visible damage and try a battery replacement first. If the backlight issue persists, buy a screen. Luckily 6s parts are cheap.
try to soft reset it. (hold home button+sleep button at the same time until you see the apple logo) If you changed the screen yourself, did you disconnect the battery while removing the screen?
Had a customer with this problem on the S6. I had to take off the back panel and remove the buttons and clean them. Set them back in and they were fine.
Take out your sim card, connect to wifi. Wait for the phone to be connected to wifi then set in your sim card. If the sim card has a lock code on it, unlock it. If it's saying no service after that then it could be something wrong with your sim card. Try another sim card if you can.
alot of times the red screen or blue screen is a result of damage to the screws in the con shield over the lcd cables(screws set in the wrong place or direct damage to the logic board in the screw hole) or your camera flex cable is broken. at least in my experience