If you hold down the option key while turning it on does that help? Try listening very closely too see if you can here any fans or start up disks spinning when you first try turning it on. Also, does the power adapter light turn green/orange while plugged in?
Have you tried doing a full teardown of the phone and thoroughly drying each piece in rice? If not do that first. Then, normally the first part to break from water damage is the battery, so you can try replacing that, and if that doesn't work the Lightning Connector Assembly is also commonly broke because of water damage. And if both those don't fix it then it's your logic board most likely.
Is there any way you could test both these screens on another iPhone 6? If they still don't work on that phone then you know it's the screens. But what I'm guessing part of the pins on the terminals to your logic board might have got bent. Look close at teach pin on the board where the cables connect and make sure it all looks correct.